LMFDB - Embedded newform 225.2.q.a.16.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(16,225)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 6]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("225.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.q (of order $15$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			16.16
Character	$\chi$	$=$	225.16
Dual form			225.2.q.a.211.16

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309584 - 0.137836i) q^{2} +(1.59476 + 0.675825i) q^{3} +(-1.26142 + 1.40095i) q^{4} +(-1.79806 + 1.32928i) q^{5} +(0.586865 - 0.0105903i) q^{6} +(0.0614798 - 0.106486i) q^{7} +(-0.406855 + 1.25217i) q^{8} +(2.08652 + 2.15556i) q^{9} +O(q^{10})$	\(q+(0.309584 - 0.137836i) q^{2} +(1.59476 + 0.675825i) q^{3} +(-1.26142 + 1.40095i) q^{4} +(-1.79806 + 1.32928i) q^{5} +(0.586865 - 0.0105903i) q^{6} +(0.0614798 - 0.106486i) q^{7} +(-0.406855 + 1.25217i) q^{8} +(2.08652 + 2.15556i) q^{9} +(-0.373429 + 0.659360i) q^{10} +(0.389945 - 0.173615i) q^{11} +(-2.95845 + 1.38168i) q^{12} +(3.49609 + 1.55656i) q^{13} +(0.00435558 - 0.0414406i) q^{14} +(-3.76583 + 0.904704i) q^{15} +(-0.347467 - 3.30593i) q^{16} +(-1.33754 + 4.11653i) q^{17} +(0.943067 + 0.379729i) q^{18} +(0.402455 - 1.23863i) q^{19} +(0.405860 - 4.19576i) q^{20} +(0.170012 - 0.128270i) q^{21} +(0.0967906 - 0.107497i) q^{22} +(0.834522 - 7.93995i) q^{23} +(-1.49508 + 1.72195i) q^{24} +(1.46605 - 4.78024i) q^{25} +1.29688 q^{26} +(1.87072 + 4.84772i) q^{27} +(0.0716297 + 0.220453i) q^{28} +(-4.68288 - 0.995377i) q^{29} +(-1.04114 + 0.799149i) q^{30} +(6.54724 - 1.39166i) q^{31} +(-1.87986 - 3.25601i) q^{32} +(0.739203 - 0.0133393i) q^{33} +(0.153323 + 1.45877i) q^{34} +(0.0310051 + 0.273192i) q^{35} +(-5.65179 + 0.204046i) q^{36} +(5.35375 - 3.88973i) q^{37} +(-0.0461337 - 0.438933i) q^{38} +(4.52347 + 4.84509i) q^{39} +(-0.932932 - 2.79230i) q^{40} +(5.82236 + 2.59228i) q^{41} +(0.0349527 - 0.0631441i) q^{42} +(-1.74377 + 3.02030i) q^{43} +(-0.248659 + 0.765293i) q^{44} +(-6.61703 - 1.10226i) q^{45} +(-0.836054 - 2.57311i) q^{46} +(-5.28842 - 1.12409i) q^{47} +(1.68010 - 5.50700i) q^{48} +(3.49244 + 6.04908i) q^{49} +(-0.205024 - 1.68196i) q^{50} +(-4.91511 + 5.66093i) q^{51} +(-6.59069 + 2.93436i) q^{52} +(-1.82854 - 5.62767i) q^{53} +(1.24734 + 1.24293i) q^{54} +(-0.470363 + 0.830516i) q^{55} +(0.108326 + 0.120308i) q^{56} +(1.47892 - 1.70333i) q^{57} +(-1.58694 + 0.337315i) q^{58} +(-5.94695 - 2.64775i) q^{59} +(3.48285 - 6.41694i) q^{60} +(9.05256 - 4.03046i) q^{61} +(1.83510 - 1.33328i) q^{62} +(0.357816 - 0.0896624i) q^{63} +(4.34781 + 3.15887i) q^{64} +(-8.35529 + 1.84848i) q^{65} +(0.227007 - 0.106018i) q^{66} +(-7.58023 + 1.61123i) q^{67} +(-4.07984 - 7.06649i) q^{68} +(6.69688 - 12.0983i) q^{69} +(0.0472544 + 0.0803024i) q^{70} +(1.29478 + 3.98492i) q^{71} +(-3.54804 + 1.73568i) q^{72} +(-8.67115 - 6.29996i) q^{73} +(1.12129 - 1.94214i) q^{74} +(5.56860 - 6.63255i) q^{75} +(1.22759 + 2.12625i) q^{76} +(0.00548619 - 0.0521976i) q^{77} +(2.06822 + 0.876467i) q^{78} +(6.30512 + 1.34020i) q^{79} +(5.01927 + 5.48239i) q^{80} +(-0.292856 + 8.99523i) q^{81} +2.15982 q^{82} +(-1.73857 - 1.93088i) q^{83} +(-0.0347558 + 0.399980i) q^{84} +(-3.06703 - 9.17973i) q^{85} +(-0.123539 + 1.17539i) q^{86} +(-6.79537 - 4.75220i) q^{87} +(0.0587443 + 0.558914i) q^{88} +(4.89782 + 3.55847i) q^{89} +(-2.20046 + 0.570821i) q^{90} +(0.380691 - 0.276588i) q^{91} +(10.0708 + 11.1847i) q^{92} +(11.3818 + 2.20542i) q^{93} +(-1.79215 + 0.380933i) q^{94} +(0.922843 + 2.76211i) q^{95} +(-0.797430 - 6.46301i) q^{96} +(-13.6699 - 2.90563i) q^{97} +(1.91498 + 1.39132i) q^{98} +(1.18787 + 0.478299i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9}+O(q^{10}) $ 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20} + 15 q^{21} - 11 q^{22} + q^{23} - 30 q^{24} - 16 q^{25} - 136 q^{26} + 7 q^{27} + 4 q^{28} - 15 q^{29} - 24 q^{30} + 3 q^{31} + 12 q^{32} - 5 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} - 24 q^{37} + 55 q^{38} + 20 q^{39} + q^{40} - 19 q^{41} - 38 q^{42} - 8 q^{43} + 4 q^{44} - 38 q^{45} - 20 q^{46} - 10 q^{47} - 25 q^{48} - 72 q^{49} - 3 q^{50} - 26 q^{51} - 25 q^{52} - 12 q^{53} + 53 q^{54} - 20 q^{55} - 60 q^{56} + 38 q^{57} - 23 q^{58} - 30 q^{59} - 33 q^{60} - 3 q^{61} - 44 q^{62} + 46 q^{63} - 44 q^{64} + 51 q^{65} - 134 q^{66} - 12 q^{67} - 156 q^{68} + 4 q^{69} - 16 q^{70} + 42 q^{71} + 74 q^{72} - 12 q^{73} + 90 q^{74} + 67 q^{75} - 8 q^{76} + 31 q^{77} - 92 q^{78} - 15 q^{79} + 298 q^{80} - 104 q^{81} + 8 q^{82} + 59 q^{83} + 115 q^{84} - 11 q^{85} + 9 q^{86} - 59 q^{87} - 23 q^{88} + 106 q^{89} + 107 q^{90} + 30 q^{91} + 11 q^{92} + 32 q^{93} + 25 q^{94} + 7 q^{95} + 35 q^{96} - 21 q^{97} + 146 q^{98} - 20 q^{99}+O(q^{100}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9 - 20 * q^10 - 11 * q^11 - 4 * q^12 - 3 * q^13 + q^14 - 48 * q^15 + 23 * q^16 - 24 * q^17 - 12 * q^19 + q^20 + 15 * q^21 - 11 * q^22 + q^23 - 30 * q^24 - 16 * q^25 - 136 * q^26 + 7 * q^27 + 4 * q^28 - 15 * q^29 - 24 * q^30 + 3 * q^31 + 12 * q^32 - 5 * q^33 + q^34 + 14 * q^35 + 38 * q^36 - 24 * q^37 + 55 * q^38 + 20 * q^39 + q^40 - 19 * q^41 - 38 * q^42 - 8 * q^43 + 4 * q^44 - 38 * q^45 - 20 * q^46 - 10 * q^47 - 25 * q^48 - 72 * q^49 - 3 * q^50 - 26 * q^51 - 25 * q^52 - 12 * q^53 + 53 * q^54 - 20 * q^55 - 60 * q^56 + 38 * q^57 - 23 * q^58 - 30 * q^59 - 33 * q^60 - 3 * q^61 - 44 * q^62 + 46 * q^63 - 44 * q^64 + 51 * q^65 - 134 * q^66 - 12 * q^67 - 156 * q^68 + 4 * q^69 - 16 * q^70 + 42 * q^71 + 74 * q^72 - 12 * q^73 + 90 * q^74 + 67 * q^75 - 8 * q^76 + 31 * q^77 - 92 * q^78 - 15 * q^79 + 298 * q^80 - 104 * q^81 + 8 * q^82 + 59 * q^83 + 115 * q^84 - 11 * q^85 + 9 * q^86 - 59 * q^87 - 23 * q^88 + 106 * q^89 + 107 * q^90 + 30 * q^91 + 11 * q^92 + 32 * q^93 + 25 * q^94 + 7 * q^95 + 35 * q^96 - 21 * q^97 + 146 * q^98 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.309584	−	0.137836i	0.218909	−	0.0974646i	−0.294352	−	0.955697i	$-0.595104\pi$
$2$	0.309584	−	0.137836i	0.218909	−	0.0974646i	0.513261	+	0.858232i	$0.328437\pi$
$3$	1.59476	+	0.675825i	0.920735	+	0.390188i
$3$	1.59476	+	0.675825i	0.920735	+	0.390188i
$4$	−1.26142	+	1.40095i	−0.630709	+	0.700473i
$5$	−1.79806	+	1.32928i	−0.804117	+	0.594471i
$5$	−1.79806	+	1.32928i	−0.804117	+	0.594471i
$6$	0.586865	−	0.0105903i	0.239587	−	0.00432348i
$7$	0.0614798	−	0.106486i	0.0232372	−	0.0402480i	−0.854173	−	0.519989i	$-0.825936\pi$
$7$	0.0614798	−	0.106486i	0.0232372	−	0.0402480i	0.877410	+	0.479741i	$0.159269\pi$
$8$	−0.406855	+	1.25217i	−0.143845	+	0.442709i
$9$	2.08652	+	2.15556i	0.695507	+	0.718519i
$10$	−0.373429	+	0.659360i	−0.118089	+	0.208508i
$11$	0.389945	−	0.173615i	0.117573	−	0.0523469i	−0.347107	−	0.937825i	$-0.612836\pi$
$11$	0.389945	−	0.173615i	0.117573	−	0.0523469i	0.464680	+	0.885479i	$0.346169\pi$
$12$	−2.95845	+	1.38168i	−0.854032	+	0.398856i
$13$	3.49609	+	1.55656i	0.969642	+	0.431712i	0.829554	−	0.558427i	$-0.188595\pi$
$13$	3.49609	+	1.55656i	0.969642	+	0.431712i	0.140088	+	0.990139i	$0.455262\pi$
$14$	0.00435558	−	0.0414406i	0.00116408	−	0.0110755i
$15$	−3.76583	+	0.904704i	−0.972334	+	0.233594i
$16$	−0.347467	−	3.30593i	−0.0868669	−	0.826483i
$17$	−1.33754	+	4.11653i	−0.324401	+	0.998405i	0.647309	+	0.762228i	$0.275895\pi$
$17$	−1.33754	+	4.11653i	−0.324401	+	0.998405i	−0.971710	+	0.236177i	$0.924105\pi$
$18$	0.943067	+	0.379729i	0.222283	+	0.0895030i
$19$	0.402455	−	1.23863i	0.0923296	−	0.284161i	−0.894219	−	0.447630i	$-0.852268\pi$
$19$	0.402455	−	1.23863i	0.0923296	−	0.284161i	0.986549	+	0.163469i	$0.0522682\pi$
$20$	0.405860	−	4.19576i	0.0907531	−	0.938200i
$21$	0.170012	−	0.128270i	0.0370996	−	0.0279909i
$22$	0.0967906	−	0.107497i	0.0206358	−	0.0229184i
$23$	0.834522	−	7.93995i	0.174010	−	1.65559i	−0.464200	−	0.885731i	$-0.653658\pi$
$23$	0.834522	−	7.93995i	0.174010	−	1.65559i	0.638210	−	0.769863i	$-0.279675\pi$
$24$	−1.49508	+	1.72195i	−0.305183	+	0.351492i
$25$	1.46605	−	4.78024i	0.293209	−	0.956048i
$26$	1.29688			0.254340
$27$	1.87072	+	4.84772i	0.360021	+	0.932944i
$28$	0.0716297	+	0.220453i	0.0135367	+	0.0416618i
$29$	−4.68288	−	0.995377i	−0.869589	−	0.184837i	−0.248553	−	0.968618i	$-0.579955\pi$
$29$	−4.68288	−	0.995377i	−0.869589	−	0.184837i	−0.621037	+	0.783782i	$0.713288\pi$
$30$	−1.04114	+	0.799149i	−0.190086	+	0.145904i
$31$	6.54724	−	1.39166i	1.17592	−	0.249949i	0.421801	−	0.906688i	$-0.361398\pi$
$31$	6.54724	−	1.39166i	1.17592	−	0.249949i	0.754118	+	0.656739i	$0.228065\pi$
$32$	−1.87986	−	3.25601i	−0.332315	−	0.575586i
$33$	0.739203	−	0.0133393i	0.128679	−	0.00232208i
$34$	0.153323	+	1.45877i	0.0262947	+	0.250178i
$35$	0.0310051	+	0.273192i	0.00524083	+	0.0461779i
$36$	−5.65179	+	0.204046i	−0.941966	+	0.0340077i
$37$	5.35375	−	3.88973i	0.880151	−	0.639467i	−0.0531405	−	0.998587i	$-0.516923\pi$
$37$	5.35375	−	3.88973i	0.880151	−	0.639467i	0.933291	+	0.359120i	$0.116923\pi$
$38$	−0.0461337	−	0.438933i	−0.00748388	−	0.0712043i
$39$	4.52347	+	4.84509i	0.724335	+	0.775835i
$40$	−0.932932	−	2.79230i	−0.147509	−	0.441502i
$41$	5.82236	+	2.59228i	0.909300	+	0.404847i	0.807438	−	0.589952i	$-0.200853\pi$
$41$	5.82236	+	2.59228i	0.909300	+	0.404847i	0.101862	+	0.994799i	$0.467520\pi$
$42$	0.0349527	−	0.0631441i	0.00539331	−	0.00974335i
$43$	−1.74377	+	3.02030i	−0.265923	+	0.460592i	−0.967805	−	0.251701i	$-0.919010\pi$
$43$	−1.74377	+	3.02030i	−0.265923	+	0.460592i	0.701882	+	0.712293i	$0.252343\pi$
$44$	−0.248659	+	0.765293i	−0.0374867	+	0.115372i
$45$	−6.61703	−	1.10226i	−0.986408	−	0.164315i
$46$	−0.836054	−	2.57311i	−0.123269	−	0.379384i
$47$	−5.28842	−	1.12409i	−0.771395	−	0.163965i	−0.194632	−	0.980876i	$-0.562351\pi$
$47$	−5.28842	−	1.12409i	−0.771395	−	0.163965i	−0.576763	+	0.816911i	$0.695685\pi$
$48$	1.68010	−	5.50700i	0.242502	−	0.794867i
$49$	3.49244	+	6.04908i	0.498920	+	0.864155i
$50$	−0.205024	−	1.68196i	−0.0289947	−	0.237865i
$51$	−4.91511	+	5.66093i	−0.688253	+	0.792689i
$52$	−6.59069	+	2.93436i	−0.913964	+	0.406923i
$53$	−1.82854	−	5.62767i	−0.251169	−	0.773019i	−0.994560	−	0.104162i	$-0.966784\pi$
$53$	−1.82854	−	5.62767i	−0.251169	−	0.773019i	0.743391	−	0.668857i	$-0.233216\pi$
$54$	1.24734	+	1.24293i	0.169741	+	0.169141i
$55$	−0.470363	+	0.830516i	−0.0634238	+	0.111987i
$56$	0.108326	+	0.120308i	0.0144756	+	0.0160768i
$57$	1.47892	−	1.70333i	0.195887	−	0.225611i
$58$	−1.58694	+	0.337315i	−0.208376	+	0.0442917i
$59$	−5.94695	−	2.64775i	−0.774226	−	0.344708i	−0.0186992	−	0.999825i	$-0.505952\pi$
$59$	−5.94695	−	2.64775i	−0.774226	−	0.344708i	−0.755527	+	0.655117i	$0.772619\pi$
$60$	3.48285	−	6.41694i	0.449634	−	0.828424i
$61$	9.05256	−	4.03046i	1.15906	−	0.516048i	0.265113	−	0.964217i	$-0.414591\pi$
$61$	9.05256	−	4.03046i	1.15906	−	0.516048i	0.893949	+	0.448170i	$0.147924\pi$
$62$	1.83510	−	1.33328i	0.233058	−	0.169327i
$63$	0.357816	−	0.0896624i	0.0450806	−	0.0112964i
$64$	4.34781	+	3.15887i	0.543476	+	0.394858i
$65$	−8.35529	+	1.84848i	−1.03635	+	0.229276i
$66$	0.227007	−	0.106018i	0.0279426	−	0.0130499i
$67$	−7.58023	+	1.61123i	−0.926072	+	0.196843i	−0.646177	−	0.763188i	$-0.723633\pi$
$67$	−7.58023	+	1.61123i	−0.926072	+	0.196843i	−0.279896	+	0.960030i	$0.590300\pi$
$68$	−4.07984	−	7.06649i	−0.494753	−	0.856937i
$69$	6.69688	−	12.0983i	0.806209	−	1.45647i
$70$	0.0472544	+	0.0803024i	0.00564798	+	0.00959797i
$71$	1.29478	+	3.98492i	0.153662	+	0.472923i	0.998023	−	0.0628518i	$-0.0200196\pi$
$71$	1.29478	+	3.98492i	0.153662	+	0.472923i	−0.844361	+	0.535775i	$0.820020\pi$
$72$	−3.54804	+	1.73568i	−0.418140	+	0.204552i
$73$	−8.67115	−	6.29996i	−1.01488	−	0.737354i	−0.0496538	−	0.998766i	$-0.515812\pi$
$73$	−8.67115	−	6.29996i	−1.01488	−	0.737354i	−0.965227	+	0.261412i	$0.915812\pi$
$74$	1.12129	−	1.94214i	0.130348	−	0.225769i
$75$	5.56860	−	6.63255i	0.643006	−	0.765861i
$76$	1.22759	+	2.12625i	0.140814	+	0.243897i
$77$	0.00548619	−	0.0521976i	0.000625209	−	0.00594847i
$78$	2.06822	+	0.876467i	0.234180	+	0.0992403i
$79$	6.30512	+	1.34020i	0.709382	+	0.150784i	0.548452	−	0.836182i	$-0.315217\pi$
$79$	6.30512	+	1.34020i	0.709382	+	0.150784i	0.160930	+	0.986966i	$0.448551\pi$
$80$	5.01927	+	5.48239i	0.561171	+	0.612950i
$81$	−0.292856	+	8.99523i	−0.0325395	+	0.999470i
$82$	2.15982			0.238512
$83$	−1.73857	−	1.93088i	−0.190833	−	0.211942i	0.640134	−	0.768263i	$-0.278879\pi$
$83$	−1.73857	−	1.93088i	−0.190833	−	0.211942i	−0.830967	+	0.556322i	$0.812212\pi$
$84$	−0.0347558	+	0.399980i	−0.00379216	+	0.0436413i
$85$	−3.06703	−	9.17973i	−0.332666	−	0.995682i
$86$	−0.123539	+	1.17539i	−0.0133215	+	0.126746i
$87$	−6.79537	−	4.75220i	−0.728540	−	0.509489i
$88$	0.0587443	+	0.558914i	0.00626216	+	0.0595805i
$89$	4.89782	+	3.55847i	0.519168	+	0.377197i	0.816290	−	0.577642i	$-0.196027\pi$
$89$	4.89782	+	3.55847i	0.519168	+	0.377197i	−0.297123	+	0.954839i	$0.596027\pi$
$90$	−2.20046	+	0.570821i	−0.231949	+	0.0601698i
$91$	0.380691	−	0.276588i	0.0399073	−	0.0289944i
$92$	10.0708	+	11.1847i	1.04995	+	1.16609i
$93$	11.3818	+	2.20542i	1.18024	+	0.228692i
$94$	−1.79215	+	0.380933i	−0.184846	+	0.0392903i
$95$	0.922843	+	2.76211i	0.0946817	+	0.283386i
$96$	−0.797430	−	6.46301i	−0.0813874	−	0.659628i
$97$	−13.6699	−	2.90563i	−1.38797	−	0.295022i	−0.547467	−	0.836827i	$-0.684408\pi$
$97$	−13.6699	−	2.90563i	−1.38797	−	0.295022i	−0.840504	+	0.541805i	$0.817741\pi$
$98$	1.91498	+	1.39132i	0.193443	+	0.140544i
$99$	1.18787	+	0.478299i	0.119385	+	0.0480708i
$100$	4.84756	+	8.08373i	0.484756	+	0.808373i
$101$	−8.64870	+	14.9800i	−0.860578	+	1.49056i	0.0107947	+	0.999942i	$0.496564\pi$
$101$	−8.64870	+	14.9800i	−0.860578	+	1.49056i	−0.871372	+	0.490622i	$0.836769\pi$
$102$	−0.741361	+	2.43001i	−0.0734057	+	0.240607i
$103$	1.27003	−	1.41052i	0.125140	−	0.138982i	−0.677319	−	0.735690i	$-0.736858\pi$
$103$	1.27003	−	1.41052i	0.125140	−	0.138982i	0.802459	+	0.596708i	$0.203525\pi$
$104$	−3.37148	+	3.74441i	−0.330601	+	0.367170i
$105$	−0.135184	+	0.456630i	−0.0131926	+	0.0445626i
$106$	−1.34178	−	1.49020i	−0.130325	−	0.144741i
$107$	5.58314			0.539742			0.269871	−	0.962896i	$-0.413019\pi$
$107$	5.58314			0.539742			0.269871	+	0.962896i	$0.413019\pi$
$108$	−9.15116	−	3.49422i	−0.880571	−	0.336231i
$109$	−10.3236	+	7.50051i	−0.988818	+	0.718419i	−0.959662	−	0.281156i	$-0.909282\pi$
$109$	−10.3236	+	7.50051i	−0.988818	+	0.718419i	−0.0291563	+	0.999575i	$0.509282\pi$
$110$	−0.0311423	+	0.321947i	−0.00296930	+	0.0306965i
$111$	11.1667	−	2.58498i	1.05990	−	0.245356i
$112$	−0.373398	−	0.166248i	−0.0352828	−	0.0157089i
$113$	0.606880	+	0.270201i	0.0570905	+	0.0254183i	0.435083	−	0.900390i	$-0.356719\pi$
$113$	0.606880	+	0.270201i	0.0570905	+	0.0254183i	−0.377993	+	0.925809i	$0.623386\pi$
$114$	0.223070	−	0.731171i	0.0208924	−	0.0684804i
$115$	9.05386	+	15.3858i	0.844277	+	1.43473i
$116$	7.30154	−	5.30488i	0.677931	−	0.492546i
$117$	3.93942	+	10.7838i	0.364199	+	0.996965i
$118$	−2.20603			−0.203082
$119$	0.356122	+	0.395513i	0.0326456	+	0.0362566i
$120$	0.399305	−	5.08355i	0.0364514	−	0.464063i
$121$	−7.23852	+	8.03919i	−0.658047	+	0.730836i
$122$	2.24699	−	2.49553i	0.203433	−	0.225935i
$123$	7.53335	+	8.06897i	0.679259	+	0.727554i
$124$	−6.30916	+	10.9278i	−0.566580	+	0.981345i
$125$	3.71822	+	10.5439i	0.332568	+	0.943079i
$126$	0.0984155	−	0.0770779i	0.00876755	−	0.00686665i
$127$	1.19275	+	0.866583i	0.105839	+	0.0768968i	0.639446	−	0.768836i	$-0.279164\pi$
$127$	1.19275	+	0.866583i	0.105839	+	0.0768968i	−0.533607	+	0.845733i	$0.679164\pi$
$128$	9.13653	+	1.94203i	0.807562	+	0.171653i
$129$	−4.82209	+	3.63817i	−0.424562	+	0.320323i
$130$	−2.33188	+	1.72392i	−0.204519	+	0.151198i
$131$	18.5605	−	3.94515i	1.62164	−	0.344689i	0.694523	−	0.719470i	$-0.255615\pi$
$131$	18.5605	−	3.94515i	1.62164	−	0.344689i	0.927113	+	0.374781i	$0.122282\pi$
$132$	−0.913756	+	1.05241i	−0.0795322	+	0.0916005i
$133$	−0.107154	−	0.119007i	−0.00929144	−	0.0103192i
$134$	−2.12463	+	1.54364i	−0.183540	+	0.133350i
$135$	−9.80764	−	6.22979i	−0.844107	−	0.536175i
$136$	−4.61041	−	3.34966i	−0.395340	−	0.287231i
$137$	−0.493146	−	4.69197i	−0.0421323	−	0.400862i	−0.995182	−	0.0980472i	$-0.968740\pi$
$137$	−0.493146	−	4.69197i	−0.0421323	−	0.400862i	0.953049	−	0.302815i	$-0.0979263\pi$
$138$	0.405665	−	4.66852i	0.0345325	−	0.397411i
$139$	1.65057	−	15.7041i	0.139999	−	1.33201i	−0.668590	−	0.743632i	$-0.733102\pi$
$139$	1.65057	−	15.7041i	0.139999	−	1.33201i	0.808589	−	0.588374i	$-0.200232\pi$
$140$	−0.421838	−	0.301173i	−0.0356518	−	0.0254538i
$141$	−7.67407	−	5.36670i	−0.646274	−	0.451957i
$142$	0.950108	+	1.05520i	0.0797313	+	0.0885505i
$143$	1.63353			0.136602
$144$	6.40113	−	7.64689i	0.533427	−	0.637240i
$145$	9.74324	−	4.43510i	0.809132	−	0.368315i
$146$	−3.55281	−	0.755173i	−0.294033	−	0.0624986i
$147$	1.48148	+	12.0071i	0.122191	+	0.990330i
$148$	−1.30402	+	12.4069i	−0.107189	+	1.01984i
$149$	−4.79434	−	8.30404i	−0.392768	−	0.680294i	0.600046	−	0.799966i	$-0.295149\pi$
$149$	−4.79434	−	8.30404i	−0.392768	−	0.680294i	−0.992813	+	0.119672i	$0.961816\pi$
$150$	0.809747	−	2.82088i	0.0661156	−	0.230324i
$151$	10.6002	−	18.3600i	0.862628	−	1.49412i	−0.00675530	−	0.999977i	$-0.502150\pi$
$151$	10.6002	−	18.3600i	0.862628	−	1.49412i	0.869383	−	0.494138i	$-0.164516\pi$
$152$	1.38724	+	1.00789i	0.112520	+	0.0817503i
$153$	−11.6642	+	5.70608i	−0.942997	+	0.461309i
$154$	−0.00549626	−	0.0169157i	−0.000442901	−	0.00136311i
$155$	−9.92244	+	11.2054i	−0.796989	+	0.900038i
$156$	−12.4937	+	0.225456i	−1.00030	+	0.0180509i
$157$	−11.5818	−	20.0603i	−0.924331	−	1.60099i	−0.792634	−	0.609698i	$-0.791291\pi$
$157$	−11.5818	−	20.0603i	−0.924331	−	1.60099i	−0.131697	−	0.991290i	$-0.542043\pi$
$158$	2.13669	−	0.454168i	0.169986	−	0.0361317i
$159$	0.887234	−	10.2106i	0.0703622	−	0.809749i
$160$	7.70823	+	3.35565i	0.609389	+	0.265287i
$161$	−0.794188	−	0.577012i	−0.0625908	−	0.0454749i
$162$	1.14920	+	2.82515i	0.0902898	+	0.221965i
$163$	−18.7433	+	13.6178i	−1.46809	+	1.06663i	−0.486931	+	0.873440i	$0.661884\pi$
$163$	−18.7433	+	13.6178i	−1.46809	+	1.06663i	−0.981161	+	0.193191i	$0.938116\pi$
$164$	−10.9761	+	4.88687i	−0.857088	+	0.381600i
$165$	−1.31140	+	1.00659i	−0.102092	+	0.0783629i
$166$	−0.804379	−	0.358133i	−0.0624319	−	0.0277965i
$167$	24.7422	−	5.25911i	1.91461	−	0.406962i	0.914609	−	0.404340i	$-0.132499\pi$
$167$	24.7422	−	5.25911i	1.91461	−	0.406962i	0.999997	−	0.00262181i	$-0.000834550\pi$
$168$	0.0914463	+	0.265071i	0.00705524	+	0.0204507i
$169$	1.10108	+	1.22288i	0.0846988	+	0.0940676i
$170$	−2.21480	−	2.41915i	−0.169867	−	0.185541i
$171$	3.50967	−	1.71691i	0.268391	−	0.131296i
$172$	−2.03165	−	6.25279i	−0.154912	−	0.476771i
$173$	0.922544	−	0.410743i	0.0701397	−	0.0312282i	−0.371367	−	0.928486i	$-0.621111\pi$
$173$	0.922544	−	0.410743i	0.0701397	−	0.0312282i	0.441507	+	0.897258i	$0.354444\pi$
$174$	−2.75876	−	0.534559i	−0.209141	−	0.0405248i
$175$	−0.418897	−	0.450002i	−0.0316657	−	0.0340170i
$176$	−0.709452	−	1.22881i	−0.0534770	−	0.0926249i
$177$	−7.69454	−	8.24162i	−0.578357	−	0.619478i
$178$	2.00677	+	0.426553i	0.150414	+	0.0319715i
$179$	0.162849	+	0.501199i	0.0121719	+	0.0374614i	0.956958	−	0.290226i	$-0.0937306\pi$
$179$	0.162849	+	0.501199i	0.0121719	+	0.0374614i	−0.944786	+	0.327688i	$0.893731\pi$
$180$	9.89104	−	7.87969i	0.737234	−	0.587317i
$181$	−4.02347	+	12.3830i	−0.299062	+	0.920418i	0.682765	+	0.730638i	$0.260777\pi$
$181$	−4.02347	+	12.3830i	−0.299062	+	0.920418i	−0.981827	+	0.189780i	$0.939223\pi$
$182$	0.0797322	−	0.138100i	0.00591015	−	0.0102367i
$183$	17.1606	−	0.309672i	1.26854	−	0.0228916i
$184$	9.60264	+	4.27537i	0.707916	+	0.315185i
$185$	−4.45584	+	14.1106i	−0.327600	+	1.03743i
$186$	3.82761	−	0.886054i	0.280654	−	0.0649686i
$187$	0.193123	+	1.83744i	0.0141225	+	0.134367i
$188$	8.24569	−	5.99084i	0.601379	−	0.436927i
$189$	0.631227	+	0.0988309i	0.0459150	+	0.00718889i
$190$	0.666415	+	0.727904i	0.0483468	+	0.0528077i
$191$	−0.991770	−	9.43606i	−0.0717620	−	0.682770i	−0.969974	−	0.243208i	$-0.921800\pi$
$191$	−0.991770	−	9.43606i	−0.0717620	−	0.682770i	0.898212	−	0.439562i	$-0.144866\pi$
$192$	4.79887	+	7.97599i	0.346329	+	0.575618i
$193$	3.15356	+	5.46213i	0.226998	+	0.393173i	0.956917	−	0.290361i	$-0.0937754\pi$
$193$	3.15356	+	5.46213i	0.226998	+	0.393173i	−0.729919	+	0.683534i	$0.760442\pi$
$194$	−4.63250	+	0.984667i	−0.332594	+	0.0706950i
$195$	−14.5739	−	2.69882i	−1.04366	−	0.193267i
$196$	−12.8799	−	2.73770i	−0.919990	−	0.195550i
$197$	−7.37768	−	22.7062i	−0.525638	−	1.61775i	−0.763052	−	0.646338i	$-0.776300\pi$
$197$	−7.37768	−	22.7062i	−0.525638	−	1.61775i	0.237414	−	0.971409i	$-0.423700\pi$
$198$	0.433671	−	0.0156568i	0.0308197	−	0.00111268i
$199$	−2.41802			−0.171409			−0.0857044	−	0.996321i	$-0.527314\pi$
$199$	−2.41802			−0.171409			−0.0857044	+	0.996321i	$0.527314\pi$
$200$	5.38921	+	3.78061i	0.381075	+	0.267329i
$201$	−13.1776	−	2.55339i	−0.929473	−	0.180102i
$202$	−0.612723	+	5.82967i	−0.0431110	+	0.410174i
$203$	−0.393897	+	0.437466i	−0.0276461	+	0.0307041i
$204$	−1.73066	−	14.0266i	−0.121170	−	0.982059i
$205$	−13.9148	+	3.07845i	−0.971854	+	0.215008i
$206$	0.198763	−	0.611729i	0.0138485	−	0.0426212i
$207$	18.8563	−	14.7680i	1.31060	−	1.02645i
$208$	3.93111	−	12.0987i	0.272573	−	0.838894i
$209$	−0.0581090	−	0.552870i	−0.00401948	−	0.0382428i
$210$	0.0210890	+	0.159999i	0.00145528	+	0.0110410i
$211$	−0.495614	+	4.71546i	−0.0341195	+	0.324625i	0.964127	+	0.265440i	$0.0855171\pi$
$211$	−0.495614	+	4.71546i	−0.0341195	+	0.324625i	−0.998247	+	0.0591858i	$0.981150\pi$
$212$	10.1906	+	4.53715i	0.699894	+	0.311613i
$213$	−0.628246	+	7.23004i	−0.0430467	+	0.495394i
$214$	1.72845	−	0.769556i	0.118155	−	0.0526058i
$215$	−0.879409	−	7.74864i	−0.0599752	−	0.528453i
$216$	−6.83129	+	0.370145i	−0.464810	+	0.0251852i
$217$	0.254331	−	0.782749i	0.0172651	−	0.0531365i
$218$	−2.16217	+	3.74500i	−0.146441	+	0.253643i
$219$	−9.57073	−	15.9071i	−0.646730	−	1.07490i
$220$	−0.570183	−	1.70658i	−0.0384417	−	0.115058i
$221$	−11.0838	+	12.3098i	−0.745577	+	0.828047i
$222$	3.10074	−	2.33944i	0.208108	−	0.157013i
$223$	−12.1303	+	5.40074i	−0.812302	+	0.361660i	−0.770479	−	0.637465i	$-0.779983\pi$
$223$	−12.1303	+	5.40074i	−0.812302	+	0.361660i	−0.0418228	+	0.999125i	$0.513316\pi$
$224$	−0.462293			−0.0308883
$225$	13.3630	−	6.81393i	0.890868	−	0.454262i
$226$	0.225124			0.0149750
$227$	3.56436	−	1.58696i	0.236575	−	0.105330i	−0.285025	−	0.958520i	$-0.592002\pi$
$227$	3.56436	−	1.58696i	0.236575	−	0.105330i	0.521600	+	0.853190i	$0.325335\pi$
$228$	0.520740	+	4.22049i	0.0344869	+	0.279509i
$229$	12.2021	−	13.5518i	0.806336	−	0.895527i	−0.189936	−	0.981797i	$-0.560828\pi$
$229$	12.2021	−	13.5518i	0.806336	−	0.895527i	0.996272	+	0.0862695i	$0.0274946\pi$
$230$	4.92365	+	3.51526i	0.324656	+	0.231789i
$231$	0.0440256	−	0.0795350i	0.00289667	−	0.00523302i
$232$	3.15164	−	5.45879i	0.206915	−	0.358387i
$233$	−5.62835	+	17.3223i	−0.368725	+	1.13482i	0.578890	+	0.815406i	$0.303486\pi$
$233$	−5.62835	+	17.3223i	−0.368725	+	1.13482i	−0.947615	+	0.319414i	$0.896514\pi$
$234$	2.70598	+	2.79551i	0.176895	+	0.182748i
$235$	11.0031	−	5.00859i	0.717765	−	0.326725i
$236$	11.2109	−	4.99143i	0.729770	−	0.324914i
$237$	9.14943	+	6.39845i	0.594319	+	0.415624i
$238$	0.164765	+	0.0733583i	0.0106802	+	0.00475511i
$239$	0.751438	−	7.14945i	0.0486065	−	0.462460i	−0.942964	−	0.332894i	$-0.891975\pi$
$239$	0.751438	−	7.14945i	0.0486065	−	0.462460i	0.991571	−	0.129566i	$-0.0413584\pi$
$240$	4.29939	+	12.1352i	0.277525	+	0.783326i
$241$	−2.06473	−	19.6446i	−0.133001	−	1.26542i	−0.833803	−	0.552062i	$-0.813841\pi$
$241$	−2.06473	−	19.6446i	−0.133001	−	1.26542i	0.700802	−	0.713355i	$-0.252825\pi$
$242$	−1.13284	+	3.48653i	−0.0728219	+	0.224123i
$243$	−6.54624	+	14.1473i	−0.419941	+	0.907551i
$244$	−5.77260	+	17.7662i	−0.369553	+	1.13737i
$245$	−14.3205	−	6.23420i	−0.914905	−	0.398289i
$246$	3.44440	+	1.45966i	0.219607	+	0.0930646i
$247$	3.33502	−	3.70392i	0.212202	−	0.235675i
$248$	−0.921183	+	8.76447i	−0.0584952	+	0.556544i
$249$	−1.46767	−	4.25426i	−0.0930098	−	0.269603i
$250$	2.60444	+	2.75173i	0.164719	+	0.174035i
$251$	−19.5044			−1.23111			−0.615554	−	0.788095i	$-0.711068\pi$
$251$	−19.5044			−1.23111			−0.615554	+	0.788095i	$0.711068\pi$
$252$	−0.325743	+	0.614383i	−0.0205199	+	0.0387025i
$253$	−1.05307	−	3.24103i	−0.0662062	−	0.203762i
$254$	0.488702	+	0.103877i	0.0306639	+	0.00651781i
$255$	1.31272	−	16.7122i	0.0822057	−	1.04656i
$256$	−7.41729	+	1.57659i	−0.463581	+	0.0985371i
$257$	−4.74368	−	8.21630i	−0.295903	−	0.512518i	0.679292	−	0.733868i	$-0.262287\pi$
$257$	−4.74368	−	8.21630i	−0.295903	−	0.512518i	−0.975194	+	0.221350i	$0.928954\pi$
$258$	−0.991373	+	1.79098i	−0.0617202	+	0.111501i
$259$	−0.0850545	−	0.809240i	−0.00528503	−	0.0502837i
$260$	7.94988	−	14.0370i	0.493031	−	0.870539i
$261$	−7.62534	−	12.1711i	−0.471997	−	0.753372i
$262$	5.20225	−	3.77965i	0.321396	−	0.233508i
$263$	−1.59141	−	15.1412i	−0.0981304	−	0.933648i	−0.927216	−	0.374527i	$-0.877805\pi$
$263$	−1.59141	−	15.1412i	−0.0981304	−	0.933648i	0.829086	−	0.559122i	$-0.188861\pi$
$264$	−0.284045	+	0.931035i	−0.0174818	+	0.0573013i
$265$	10.7686	+	7.68825i	0.661507	+	0.472286i
$266$	−0.0495766	−	0.0220729i	−0.00303974	−	0.00135338i
$267$	5.40594	+	8.98498i	0.330838	+	0.549872i
$268$	7.30459	−	12.6519i	0.446199	−	0.772839i
$269$	−8.06733	+	24.8287i	−0.491874	+	1.51383i	0.329898	+	0.944016i	$0.392986\pi$
$269$	−8.06733	+	24.8287i	−0.491874	+	1.51383i	−0.821772	+	0.569816i	$0.807014\pi$
$270$	−3.89498	−	0.576801i	−0.237041	−	0.0351030i
$271$	−4.05570	−	12.4822i	−0.246366	−	0.758237i	−0.995409	−	0.0957154i	$-0.969486\pi$
$271$	−4.05570	−	12.4822i	−0.246366	−	0.758237i	0.749042	−	0.662522i	$-0.230514\pi$
$272$	14.0737	+	2.99146i	0.853345	+	0.181384i
$273$	0.794037	−	0.183812i	0.0480573	−	0.0111248i
$274$	−0.799391	−	1.38459i	−0.0482930	−	0.0836459i
$275$	−0.258243	−	2.11856i	−0.0155726	−	0.127754i
$276$	8.50154	+	24.6430i	0.511733	+	1.48333i
$277$	−22.8803	+	10.1870i	−1.37475	+	0.612077i	−0.955282	−	0.295695i	$-0.904449\pi$
$277$	−22.8803	+	10.1870i	−1.37475	+	0.612077i	−0.419464	+	0.907772i	$0.637782\pi$
$278$	−1.65360	−	5.08925i	−0.0991762	−	0.305233i
$279$	16.6608	+	11.2092i	0.997453	+	0.671079i
$280$	−0.354698	−	0.0723259i	−0.0211973	−	0.00432230i
$281$	5.41095	+	6.00947i	0.322790	+	0.358495i	0.882599	−	0.470127i	$-0.155792\pi$
$281$	5.41095	+	6.00947i	0.322790	+	0.358495i	−0.559808	+	0.828622i	$0.689125\pi$
$282$	−3.11549	−	0.603682i	−0.185525	−	0.0359488i
$283$	−7.85414	+	1.66945i	−0.466880	+	0.0992385i	−0.435344	−	0.900264i	$-0.643373\pi$
$283$	−7.85414	+	1.66945i	−0.466880	+	0.0992385i	−0.0315362	+	0.999503i	$0.510040\pi$
$284$	−7.21592	−	3.21273i	−0.428186	−	0.190641i
$285$	−0.394987	+	5.02858i	−0.0233970	+	0.297867i
$286$	0.505714	−	0.225158i	0.0299035	−	0.0133139i
$287$	0.634000	−	0.460628i	0.0374238	−	0.0271900i
$288$	3.09615	−	10.8459i	0.182442	−	0.639099i
$289$	−1.40351	−	1.01971i	−0.0825595	−	0.0599830i
$290$	2.40504	−	2.71600i	0.141229	−	0.159489i
$291$	−19.8366	−	13.8723i	−1.16284	−	0.813207i
$292$	19.7638	−	4.20093i	1.15659	−	0.245841i
$293$	−6.09056	−	10.5492i	−0.355814	−	0.616288i	0.631443	−	0.775423i	$-0.282463\pi$
$293$	−6.09056	−	10.5492i	−0.355814	−	0.616288i	−0.987257	+	0.159134i	$0.949130\pi$
$294$	2.11365	+	3.51301i	0.123271	+	0.204883i
$295$	14.2126	−	3.14432i	0.827487	−	0.183069i
$296$	2.69240	+	8.28636i	0.156493	+	0.481635i
$297$	1.57112	+	1.56556i	0.0911654	+	0.0908431i
$298$	−2.62885	−	1.90997i	−0.152285	−	0.110642i
$299$	15.2766	−	26.4598i	0.883467	−	1.53021i
$300$	2.26752	+	16.1677i	0.130915	+	0.933444i
$301$	0.214414	+	0.371375i	0.0123586	+	0.0214057i
$302$	0.750974	−	7.14504i	0.0432137	−	0.411151i
$303$	−23.9164	+	18.0445i	−1.37396	+	1.03663i
$304$	−4.23467	−	0.900106i	−0.242875	−	0.0516246i
$305$	−10.9195	+	19.2804i	−0.625247	+	1.10399i
$306$	−2.82456	+	3.37426i	−0.161469	+	0.192894i
$307$	24.0437			1.37225			0.686124	−	0.727485i	$-0.259311\pi$
$307$	24.0437			1.37225			0.686124	+	0.727485i	$0.259311\pi$
$308$	0.0662057	+	0.0735288i	0.00377242	+	0.00418969i
$309$	2.97866	−	1.39111i	0.169450	−	0.0791377i
$310$	−1.52733	+	4.83667i	−0.0867463	+	0.274705i
$311$	−1.78299	+	16.9640i	−0.101104	+	0.961942i	0.819931	+	0.572462i	$0.194012\pi$
$311$	−1.78299	+	16.9640i	−0.101104	+	0.961942i	−0.921035	+	0.389479i	$0.872655\pi$
$312$	−7.90727	+	3.69291i	−0.447661	+	0.209070i
$313$	0.995689	+	9.47335i	0.0562797	+	0.535465i	0.985946	+	0.167063i	$0.0534284\pi$
$313$	0.995689	+	9.47335i	0.0562797	+	0.535465i	−0.929667	+	0.368402i	$0.879905\pi$
$314$	−6.35058	−	4.61397i	−0.358384	−	0.260381i
$315$	−0.524189	+	0.636855i	−0.0295347	+	0.0358827i
$316$	−9.83094	+	7.14259i	−0.553033	+	0.401802i
$317$	−2.07800	−	2.30786i	−0.116712	−	0.129622i	0.681957	−	0.731392i	$-0.261129\pi$
$317$	−2.07800	−	2.30786i	−0.116712	−	0.129622i	−0.798669	+	0.601770i	$0.794462\pi$
$318$	−1.13271	−	3.28332i	−0.0635190	−	0.184119i
$319$	−1.99888	+	0.424875i	−0.111916	+	0.0237884i
$320$	−12.0166	+	0.0996046i	−0.671750	+	0.00556807i
$321$	8.90377	+	3.77322i	0.496960	+	0.210601i
$322$	−0.325401	−	0.0691661i	−0.0181339	−	0.00385448i
$323$	4.56056	+	3.31344i	0.253756	+	0.184365i
$324$	−12.2324	−	11.7570i	−0.679579	−	0.653168i
$325$	12.5662	−	14.4302i	0.697046	−	0.800442i
$326$	−3.92562	+	6.79937i	−0.217420	+	0.376582i
$327$	−21.5326	+	4.98459i	−1.19076	+	0.275649i
$328$	−5.61484	+	6.23591i	−0.310028	+	0.344321i
$329$	−0.444831	+	0.494035i	−0.0245243	+	0.0272370i
$330$	−0.267245	+	0.492382i	−0.0147113	+	0.0271047i
$331$	12.9126	+	14.3409i	0.709743	+	0.788249i	0.984895	−	0.173151i	$-0.0553949\pi$
$331$	12.9126	+	14.3409i	0.709743	+	0.788249i	−0.275152	+	0.961401i	$0.588728\pi$
$332$	4.89813			0.268820
$333$	19.5552	+	3.42432i	1.07162	+	0.187651i
$334$	6.93489	−	5.03849i	0.379460	−	0.275694i
$335$	11.4879	−	12.9733i	0.627654	−	0.708808i
$336$	−0.483127	−	0.517477i	−0.0263567	−	0.0282307i
$337$	−5.82074	−	2.59156i	−0.317076	−	0.141171i	0.242027	−	0.970270i	$-0.422188\pi$
$337$	−5.82074	−	2.59156i	−0.317076	−	0.141171i	−0.559103	+	0.829098i	$0.688854\pi$
$338$	0.509435	+	0.226815i	0.0277096	+	0.0123371i
$339$	0.785221	+	0.841050i	0.0426473	+	0.0456796i
$340$	16.7291	+	7.28274i	0.907264	+	0.394962i
$341$	2.31145	−	1.67937i	0.125172	−	0.0909429i
$342$	0.849886	−	1.01529i	0.0459566	−	0.0549004i
$343$	1.71958			0.0928484
$344$	−3.07247	−	3.41233i	−0.165657	−	0.183980i
$345$	4.04063	+	30.6555i	0.217540	+	1.65044i
$346$	0.228990	−	0.254319i	0.0123106	−	0.0136723i
$347$	−19.2039	+	21.3280i	−1.03092	+	1.14495i	−0.0416050	+	0.999134i	$0.513247\pi$
$347$	−19.2039	+	21.3280i	−1.03092	+	1.14495i	−0.989312	+	0.145815i	$0.953420\pi$
$348$	15.2294	−	3.52545i	0.816380	−	0.188984i
$349$	5.47421	−	9.48161i	0.293028	−	0.507539i	−0.681496	−	0.731821i	$-0.738671\pi$
$349$	5.47421	−	9.48161i	0.293028	−	0.507539i	0.974524	+	0.224283i	$0.0720038\pi$
$350$	−0.191710	−	0.0815745i	−0.0102473	−	0.00436034i
$351$	−1.00555	+	19.8600i	−0.0536724	+	1.06005i
$352$	−1.29833	−	0.943294i	−0.0692014	−	0.0502777i
$353$	2.12687	+	0.452080i	0.113202	+	0.0240618i	0.264164	−	0.964478i	$-0.414904\pi$
$353$	2.12687	+	0.452080i	0.113202	+	0.0240618i	−0.150962	+	0.988540i	$0.548237\pi$
$354$	−3.51810	−	1.49089i	−0.186985	−	0.0792401i
$355$	−7.62515	−	5.44401i	−0.404701	−	0.288938i
$356$	−11.1634	+	2.37286i	−0.591660	+	0.125761i
$357$	0.300631	+	0.871425i	0.0159111	+	0.0461207i
$358$	0.119499	+	0.132717i	0.00631570	+	0.00701430i
$359$	17.1324	−	12.4474i	0.904214	−	0.656950i	−0.0353305	−	0.999376i	$-0.511248\pi$
$359$	17.1324	−	12.4474i	0.904214	−	0.656950i	0.939545	+	0.342425i	$0.111248\pi$
$360$	4.07239	−	7.83719i	0.214634	−	0.413056i
$361$	13.9991	+	10.1709i	0.736794	+	0.535312i
$362$	0.461213	+	4.38815i	0.0242408	+	0.230636i
$363$	−16.9768	+	7.92861i	−0.891051	+	0.416144i
$364$	−0.0927252	+	0.882222i	−0.00486012	+	0.0462410i
$365$	23.9656	−	0.198649i	1.25442	−	0.0103977i
$366$	5.26995	−	2.46121i	0.275465	−	0.128649i
$367$	11.5987	+	12.8816i	0.605446	+	0.672416i	0.965466	−	0.260528i	$-0.0838968\pi$
$367$	11.5987	+	12.8816i	0.605446	+	0.672416i	−0.360020	+	0.932945i	$0.617230\pi$
$368$	−26.5389			−1.38344
$369$	6.56067	+	17.9593i	0.341535	+	0.934923i
$370$	0.565484	+	4.98259i	0.0293981	+	0.259032i
$371$	−0.711687	−	0.151274i	−0.0369489	−	0.00785374i
$372$	−17.4469	+	13.1633i	−0.904579	+	0.682486i
$373$	−2.46255	+	23.4296i	−0.127506	+	1.21314i	0.724375	+	0.689406i	$0.242128\pi$
$373$	−2.46255	+	23.4296i	−0.127506	+	1.21314i	−0.851882	+	0.523734i	$0.824538\pi$
$374$	0.313052	+	0.542223i	0.0161876	+	0.0280377i
$375$	−1.19618	+	19.3279i	−0.0617707	+	0.998090i
$376$	3.55917	−	6.16466i	0.183550	−	0.317918i
$377$	−14.8224	−	10.7691i	−0.763393	−	0.554638i
$378$	0.209040	−	0.0564092i	0.0107519	−	0.00290137i
$379$	3.41562	+	10.5122i	0.175449	+	0.539976i	0.999654	−	0.0263158i	$-0.00837755\pi$
$379$	3.41562	+	10.5122i	0.175449	+	0.539976i	−0.824205	+	0.566292i	$0.808378\pi$
$380$	−5.03365	−	2.19132i	−0.258221	−	0.112412i
$381$	1.31649	+	2.18808i	0.0674458	+	0.112099i
$382$	−1.60766	−	2.78455i	−0.0822552	−	0.142470i
$383$	−12.8825	+	2.73825i	−0.658263	+	0.139918i	−0.524920	−	0.851152i	$-0.675905\pi$
$383$	−12.8825	+	2.73825i	−0.658263	+	0.139918i	−0.133343	+	0.991070i	$0.542571\pi$
$384$	13.2581	+	9.27176i	0.676575	+	0.473148i
$385$	0.0595206	+	0.101147i	0.00303345	+	0.00515494i
$386$	1.72917	+	1.25632i	0.0880125	+	0.0639448i
$387$	−10.1488	+	2.54312i	−0.515895	+	0.129274i
$388$	21.3141	−	15.4856i	1.08206	−	0.786163i
$389$	−1.81186	+	0.806690i	−0.0918647	+	0.0409008i	−0.452155	−	0.891940i	$-0.649344\pi$
$389$	−1.81186	+	0.806690i	−0.0918647	+	0.0409008i	0.360290	+	0.932840i	$0.382678\pi$
$390$	−4.88385	+	1.17330i	−0.247304	+	0.0594122i
$391$	31.5688	+	14.0553i	1.59650	+	0.710809i
$392$	−8.99541	+	1.91203i	−0.454337	+	0.0965722i
$393$	32.2657	+	6.25206i	1.62759	+	0.315375i
$394$	−5.41373	−	6.01256i	−0.272740	−	0.302908i
$395$	−13.1185	+	5.97150i	−0.660063	+	0.300459i
$396$	−2.16847	+	1.06080i	−0.108970	+	0.0533073i
$397$	2.33072	+	7.17321i	0.116975	+	0.360013i	0.992354	−	0.123425i	$-0.0393879\pi$
$397$	2.33072	+	7.17321i	0.116975	+	0.360013i	−0.875379	+	0.483438i	$0.839388\pi$
$398$	−0.748580	+	0.333290i	−0.0375229	+	0.0167063i
$399$	−0.0904574	−	0.262205i	−0.00452854	−	0.0131266i
$400$	−16.3126	−	3.18567i	−0.815628	−	0.159284i
$401$	−12.4405	−	21.5475i	−0.621247	−	1.07603i	−0.989254	−	0.146208i	$-0.953293\pi$
$401$	−12.4405	−	21.5475i	−0.621247	−	1.07603i	0.368007	−	0.929823i	$-0.380040\pi$
$402$	−4.43151	+	1.02585i	−0.221024	+	0.0511648i
$403$	25.0560	+	5.32581i	1.24813	+	0.265297i
$404$	−10.0765	−	31.0124i	−0.501326	−	1.54292i
$405$	−11.4306	−	16.5633i	−0.567990	−	0.823035i
$406$	−0.0616456	+	0.189726i	−0.00305942	+	0.00941593i
$407$	1.41236	−	2.44627i	0.0700079	−	0.121257i
$408$	−5.08872	−	8.45774i	−0.251929	−	0.418721i
$409$	−0.705825	−	0.314253i	−0.0349008	−	0.0155388i	0.389212	−	0.921148i	$-0.372747\pi$
$409$	−0.705825	−	0.314253i	−0.0349008	−	0.0155388i	−0.424113	+	0.905609i	$0.639414\pi$
$410$	−3.88349	+	2.87100i	−0.191792	+	0.141789i
$411$	2.38450	−	7.81584i	0.117619	−	0.385527i
$412$	0.374013	+	3.55850i	0.0184263	+	0.175315i
$413$	−0.647566	+	0.470484i	−0.0318646	+	0.0231510i
$414$	3.80204	−	7.17101i	0.186860	−	0.352436i
$415$	5.69274	+	1.16080i	0.279445	+	0.0569813i
$416$	−1.50398	−	14.3094i	−0.0737387	−	0.701577i
$417$	13.2455	−	23.9288i	0.648635	−	1.17180i
$418$	−0.0941949	−	0.163150i	−0.00460722	−	0.00797995i
$419$	15.8947	−	3.37853i	0.776508	−	0.165052i	0.197422	−	0.980319i	$-0.436743\pi$
$419$	15.8947	−	3.37853i	0.776508	−	0.165052i	0.579086	+	0.815267i	$0.303410\pi$
$420$	−0.469191	−	0.765388i	−0.0228942	−	0.0373471i
$421$	−34.5725	−	7.34862i	−1.68496	−	0.358150i	−0.736843	−	0.676064i	$-0.763684\pi$
$421$	−34.5725	−	7.34862i	−1.68496	−	0.358150i	−0.948119	+	0.317914i	$0.897018\pi$
$422$	0.496524	+	1.52814i	0.0241704	+	0.0743889i
$423$	−8.61136	−	13.7449i	−0.418699	−	0.668301i
$424$	7.79075			0.378352
$425$	17.7171	+	12.4288i	0.859406	+	0.602885i
$426$	0.802063	+	2.32490i	0.0388601	+	0.112642i
$427$	0.127362	−	1.21176i	0.00616346	−	0.0586414i
$428$	−7.04267	+	7.82168i	−0.340420	+	0.378075i
$429$	2.60508	+	1.10398i	0.125775	+	0.0533006i
$430$	−1.34029	−	2.27764i	−0.0646346	−	0.109838i
$431$	7.49818	−	23.0770i	0.361175	−	1.11158i	−0.591167	−	0.806549i	$-0.701333\pi$
$431$	7.49818	−	23.0770i	0.361175	−	1.11158i	0.952342	−	0.305033i	$-0.0986674\pi$
$432$	15.3762	−	7.86891i	0.739789	−	0.378593i
$433$	5.46825	−	16.8296i	0.262788	−	0.808777i	−0.729407	−	0.684080i	$-0.760204\pi$
$433$	5.46825	−	16.8296i	0.262788	−	0.808777i	0.992195	−	0.124697i	$-0.0397960\pi$
$434$	−0.0291541	−	0.277383i	−0.00139944	−	0.0133148i
$435$	18.5355	−	0.488195i	0.888708	−	0.0234072i
$436$	2.51452	−	23.9240i	0.120424	−	1.14575i
$437$	−9.49880	−	4.22914i	−0.454389	−	0.202307i
$438$	−5.15551	−	3.60540i	−0.246340	−	0.172273i
$439$	−20.8316	+	9.27485i	−0.994240	+	0.442664i	−0.838363	−	0.545112i	$-0.816487\pi$
$439$	−20.8316	+	9.27485i	−0.994240	+	0.442664i	−0.155877	+	0.987776i	$0.549820\pi$
$440$	−0.848578	−	0.926875i	−0.0404544	−	0.0441870i
$441$	−5.75210	+	20.1497i	−0.273909	+	0.959510i
$442$	−1.73464	+	5.33866i	−0.0825083	+	0.253934i
$443$	2.91266	−	5.04488i	0.138385	−	0.239690i	−0.788501	−	0.615034i	$-0.789142\pi$
$443$	2.91266	−	5.04488i	0.138385	−	0.239690i	0.926885	+	0.375344i	$0.122476\pi$
$444$	−10.4645	+	18.9047i	−0.496622	+	0.897178i
$445$	−13.5368	+	0.112205i	−0.641705	+	0.00531902i
$446$	−3.01092	+	3.34397i	−0.142571	+	0.158341i
$447$	−2.03375	−	16.4831i	−0.0961930	−	0.779624i
$448$	0.603678	−	0.268775i	0.0285211	−	0.0126984i
$449$	−3.53148			−0.166661			−0.0833305	−	0.996522i	$-0.526556\pi$
$449$	−3.53148			−0.166661			−0.0833305	+	0.996522i	$0.526556\pi$
$450$	3.19778	−	3.95139i	0.150745	−	0.186270i
$451$	2.72046			0.128102
$452$	−1.14407	+	0.509371i	−0.0538123	+	0.0239588i
$453$	29.3128	−	22.1160i	1.37724	−	1.03910i
$454$	0.884731	−	0.982593i	0.0415225	−	0.0461154i
$455$	−0.316844	+	1.00337i	−0.0148539	+	0.0470386i
$456$	1.53115	+	2.54486i	0.0717029	+	0.119174i
$457$	1.60834	−	2.78572i	0.0752349	−	0.130311i	−0.825953	−	0.563738i	$-0.809363\pi$
$457$	1.60834	−	2.78572i	0.0752349	−	0.130311i	0.901188	+	0.433428i	$0.142696\pi$
$458$	1.90965	−	5.87730i	0.0892321	−	0.274628i
$459$	−22.4580	+	1.21686i	−1.04825	+	0.0567981i
$460$	−32.9754	−	6.72396i	−1.53749	−	0.313506i
$461$	14.5922	−	6.49685i	0.679625	−	0.302588i	−0.0377386	−	0.999288i	$-0.512015\pi$
$461$	14.5922	−	6.49685i	0.679625	−	0.302588i	0.717363	+	0.696699i	$0.245349\pi$
$462$	0.00266686	−	0.0306911i	0.000124074	−	0.00142788i
$463$	−11.7609	−	5.23629i	−0.546575	−	0.243351i	0.114823	−	0.993386i	$-0.463370\pi$
$463$	−11.7609	−	5.23629i	−0.546575	−	0.243351i	−0.661398	+	0.750035i	$0.730037\pi$
$464$	−1.66350	+	15.8271i	−0.0772261	+	0.734757i
$465$	−23.3968	+	11.1641i	−1.08500	+	0.517721i
$466$	0.645181	+	6.13849i	0.0298874	+	0.284360i
$467$	−3.12523	+	9.61848i	−0.144619	+	0.445090i	−0.996962	−	0.0778927i	$-0.975181\pi$
$467$	−3.12523	+	9.61848i	−0.144619	+	0.445090i	0.852343	+	0.522983i	$0.175181\pi$
$468$	−20.0768	−	8.08400i	−0.928051	−	0.373683i
$469$	−0.294458	+	0.906248i	−0.0135968	+	0.0418466i
$470$	2.71603	−	3.06720i	0.125281	−	0.141480i
$471$	−4.91298	−	39.8187i	−0.226378	−	1.83475i
$472$	5.73498	−	6.36934i	0.263974	−	0.293173i
$473$	−0.155607	+	1.48050i	−0.00715480	+	0.0680733i
$474$	3.71445	+	0.719741i	0.170610	+	0.0330588i
$475$	−5.33093	−	3.73972i	−0.244600	−	0.171590i
$476$	−1.00331			−0.0459867
$477$	8.31547	−	15.6838i	0.380739	−	0.718111i
$478$	−0.752817	−	2.31693i	−0.0344330	−	0.105974i
$479$	12.2773	+	2.60961i	0.560962	+	0.119236i	0.479662	−	0.877453i	$-0.340759\pi$
$479$	12.2773	+	2.60961i	0.560962	+	0.119236i	0.0813004	+	0.996690i	$0.474093\pi$
$480$	10.0250	+	10.5609i	0.457574	+	0.482036i
$481$	24.7718	−	5.26541i	1.12950	−	0.240082i
$482$	−3.34693	−	5.79705i	−0.152448	−	0.264048i
$483$	−0.876581	−	1.45693i	−0.0398858	−	0.0662925i
$484$	−2.13168	−	20.2816i	−0.0968944	−	0.921889i
$485$	28.4418	−	12.9466i	1.29147	−	0.587876i
$486$	−0.0766043	+	5.28209i	−0.00347484	+	0.239601i
$487$	−11.3262	+	8.22898i	−0.513240	+	0.372891i	−0.814051	−	0.580793i	$-0.802743\pi$
$487$	−11.3262	+	8.22898i	−0.513240	+	0.372891i	0.300811	+	0.953684i	$0.402743\pi$
$488$	1.36375	+	12.9752i	0.0617339	+	0.587358i
$489$	−39.0944	+	9.04997i	−1.76791	+	0.409254i
$490$	−5.29270	+	0.0438707i	−0.239100	+	0.00198188i
$491$	21.1245	+	9.40525i	0.953337	+	0.424453i	0.823648	−	0.567102i	$-0.191935\pi$
$491$	21.1245	+	9.40525i	0.953337	+	0.424453i	0.129689	+	0.991555i	$0.458602\pi$
$492$	−20.8069	+	0.375472i	−0.938047	+	0.0169276i
$493$	10.3610	−	17.9459i	0.466638	−	0.808241i
$494$	0.521938	−	1.60636i	0.0234831	−	0.0722736i
$495$	−2.77165	+	0.718993i	−0.124576	+	0.0323163i
$496$	−6.87568	−	21.1612i	−0.308727	−	0.950165i
$497$	0.503942	+	0.107116i	0.0226049	+	0.00480481i
$498$	−1.04076	−	1.11476i	−0.0466374	−	0.0499534i
$499$	12.0848	+	20.9314i	0.540988	+	0.937019i	0.998848	+	0.0479947i	$0.0152831\pi$
$499$	12.0848	+	20.9314i	0.540988	+	0.937019i	−0.457859	+	0.889025i	$0.651384\pi$
$500$	−19.4617	−	8.09129i	−0.870355	−	0.361853i
$501$	43.0120	+	8.33435i	1.92164	+	0.372351i
$502$	−6.03825	+	2.68840i	−0.269500	+	0.119989i
$503$	−11.4270	−	35.1686i	−0.509503	−	1.56809i	−0.793066	−	0.609136i	$-0.791516\pi$
$503$	−11.4270	−	35.1686i	−0.509503	−	1.56809i	0.283563	−	0.958954i	$-0.408484\pi$
$504$	−0.0333066	+	0.484527i	−0.00148359	+	0.0215825i
$505$	−4.36166	−	38.4314i	−0.194091	−	1.71018i
$506$	−0.772745	−	0.858220i	−0.0343527	−	0.0381526i
$507$	0.929515	+	2.69434i	0.0412812	+	0.119660i
$508$	−2.71859	+	0.577854i	−0.120618	+	0.0256381i
$509$	14.0221	+	6.24303i	0.621517	+	0.276717i	0.693239	−	0.720707i	$-0.256183\pi$
$509$	14.0221	+	6.24303i	0.621517	+	0.276717i	−0.0717222	+	0.997425i	$0.522850\pi$
$510$	−1.89715	−	5.35479i	−0.0840071	−	0.237114i
$511$	−1.20396	+	0.536037i	−0.0532600	+	0.0237129i
$512$	−17.1924	+	12.4910i	−0.759806	+	0.552031i
$513$	6.75741	−	0.366142i	0.298347	−	0.0161656i
$514$	−2.60107	−	1.88979i	−0.114728	−	0.0833549i
$515$	−0.408633	+	4.22442i	−0.0180065	+	0.186150i
$516$	0.985789	−	11.3447i	0.0433969	−	0.499425i
$517$	−2.25735	+	0.479815i	−0.0992783	+	0.0211022i
$518$	−0.137874	−	0.238804i	−0.00605782	−	0.0104925i
$519$	1.74883	−	0.0315586i	0.0767650	−	0.00138527i
$520$	1.08477	−	11.2143i	0.0475704	−	0.491780i
$521$	12.3143	+	37.8996i	0.539501	+	1.66041i	0.733718	+	0.679454i	$0.237783\pi$
$521$	12.3143	+	37.8996i	0.539501	+	1.66041i	−0.194217	+	0.980959i	$0.562217\pi$
$522$	−4.03830	−	2.71693i	−0.176751	−	0.118917i
$523$	−12.7772	−	9.28318i	−0.558708	−	0.405925i	0.272278	−	0.962219i	$-0.412223\pi$
$523$	−12.7772	−	9.28318i	−0.558708	−	0.405925i	−0.830986	+	0.556293i	$0.812223\pi$
$524$	−17.8856	+	30.9787i	−0.781335	+	1.35331i
$525$	−0.363918	−	1.00075i	−0.0158827	−	0.0436762i
$526$	−2.57968	−	4.46813i	−0.112479	−	0.194820i
$527$	−3.02840	+	28.8133i	−0.131919	+	1.25513i
$528$	−0.300948	−	2.43912i	−0.0130971	−	0.106149i
$529$	−39.8489	−	8.47015i	−1.73256	−	0.368267i
$530$	4.39349	+	0.895869i	0.190841	+	0.0389141i
$531$	−6.70105	−	18.3436i	−0.290801	−	0.796043i
$532$	0.301888			0.0130885
$533$	16.3205	+	18.1257i	0.706918	+	0.785112i
$534$	2.91205	+	2.03648i	0.126017	+	0.0881269i
$535$	−10.0388	+	7.42154i	−0.434016	+	0.320861i
$536$	1.06652	−	10.1473i	0.0460667	−	0.438296i
$537$	−0.0790169	+	0.909350i	−0.00340983	+	0.0392413i
$538$	0.924764	+	8.79854i	0.0398694	+	0.379332i
$539$	2.41207	+	1.75247i	0.103895	+	0.0754844i
$540$	21.0991	−	5.88161i	0.907962	−	0.253104i
$541$	−31.8454	+	23.1370i	−1.36914	+	0.994738i	−0.371335	+	0.928499i	$0.621100\pi$
$541$	−31.8454	+	23.1370i	−1.36914	+	0.994738i	−0.997804	+	0.0662387i	$0.978900\pi$
$542$	−2.97607	−	3.30526i	−0.127833	−	0.141973i
$543$	−14.7852	+	17.0287i	−0.634493	+	0.730771i
$544$	15.9178	−	3.38344i	0.682472	−	0.145064i
$545$	8.59215	−	27.2092i	0.368047	−	1.16552i
$546$	0.220485	−	0.166352i	0.00943590	−	0.00711920i
$547$	13.9548	+	2.96619i	0.596666	+	0.126825i	0.496338	−	0.868129i	$-0.334678\pi$
$547$	13.9548	+	2.96619i	0.596666	+	0.126825i	0.100328	+	0.994954i	$0.468011\pi$
$548$	7.19526	+	5.22766i	0.307366	+	0.223315i
$549$	27.5763	+	11.1037i	1.17693	+	0.473893i
$550$	−0.371961	−	0.620278i	−0.0158605	−	0.0264487i
$551$	−3.11755	+	5.39976i	−0.132812	+	0.230038i
$552$	12.4245	+	13.3079i	0.528822	+	0.566422i
$553$	0.530350	−	0.589014i	0.0225528	−	0.0250474i
$554$	−5.67926	+	6.30746i	−0.241289	+	0.267978i
$555$	−16.6423	+	19.4916i	−0.706426	+	0.827373i
$556$	19.9186	+	22.1218i	0.844735	+	0.938173i
$557$	15.7210			0.666119			0.333060	−	0.942906i	$-0.391919\pi$
$557$	15.7210			0.666119			0.333060	+	0.942906i	$0.391919\pi$
$558$	6.70294	+	1.17375i	0.283758	+	0.0496888i
$559$	−10.7977	+	7.84497i	−0.456693	+	0.331807i
$560$	0.892382	−	0.197426i	0.0377100	−	0.00834279i
$561$	−0.933803	+	3.06079i	−0.0394252	+	0.129227i
$562$	2.50347	+	1.11461i	0.105602	+	0.0470172i
$563$	37.1944	+	16.5600i	1.56756	+	0.697921i	0.992731	−	0.120356i	$-0.0384036\pi$
$563$	37.1944	+	16.5600i	1.56756	+	0.697921i	0.574825	+	0.818277i	$0.305070\pi$
$564$	17.1987	−	3.98132i	0.724194	−	0.167644i
$565$	−1.45038	+	0.320875i	−0.0610179	+	0.0134993i
$566$	−2.20141	+	1.59942i	−0.0925321	+	0.0672285i
$567$	0.939863	+	0.584210i	0.0394706	+	0.0245345i
$568$	−5.51659			−0.231471
$569$	8.75999	+	9.72896i	0.367238	+	0.407859i	0.898236	−	0.439514i	$-0.144849\pi$
$569$	8.75999	+	9.72896i	0.367238	+	0.407859i	−0.530998	+	0.847373i	$0.678183\pi$
$570$	0.570836	+	1.61121i	0.0239097	+	0.0674862i
$571$	−6.77500	+	7.52440i	−0.283525	+	0.314886i	−0.868038	−	0.496498i	$-0.834619\pi$
$571$	−6.77500	+	7.52440i	−0.283525	+	0.314886i	0.584513	+	0.811384i	$0.301286\pi$
$572$	−2.06056	+	2.28848i	−0.0861563	+	0.0956863i
$573$	4.79549	−	15.7185i	0.200334	−	0.656651i
$574$	0.132785	−	0.229991i	0.00554236	−	0.00959964i
$575$	−36.7314	−	15.6295i	−1.53181	−	0.651797i
$576$	2.26267	+	15.9630i	0.0942781	+	0.665125i
$577$	24.7873	+	18.0090i	1.03191	+	0.749725i	0.968690	−	0.248275i	$-0.0798635\pi$
$577$	24.7873	+	18.0090i	1.03191	+	0.749725i	0.0632185	+	0.998000i	$0.479863\pi$
$578$	−0.575057	−	0.122232i	−0.0239192	−	0.00508419i
$579$	1.33773	+	10.8420i	0.0555943	+	0.450580i
$580$	−6.07696	+	19.2443i	−0.252332	+	0.799074i
$581$	−0.312499	+	0.0664238i	−0.0129647	+	0.00275572i
$582$	−8.05318	−	1.56045i	−0.333815	−	0.0646826i
$583$	−1.69008	−	1.87702i	−0.0699959	−	0.0777383i
$584$	11.4165	−	8.29459i	0.472419	−	0.343233i
$585$	−21.4180	−	14.1534i	−0.885525	−	0.585171i
$586$	−3.33959	−	2.42636i	−0.137957	−	0.100232i
$587$	−3.51107	−	33.4056i	−0.144917	−	1.37880i	−0.789259	−	0.614060i	$-0.789535\pi$
$587$	−3.51107	−	33.4056i	−0.144917	−	1.37880i	0.644342	−	0.764738i	$-0.277131\pi$
$588$	−18.6901	−	13.0705i	−0.770767	−	0.539019i
$589$	0.911221	−	8.66969i	0.0375462	−	0.357228i
$590$	3.96658	−	2.93243i	0.163302	−	0.120726i
$591$	3.57976	−	41.1969i	0.147251	−	1.69461i
$592$	−14.7194	−	16.3476i	−0.604965	−	0.671881i
$593$	21.1167			0.867157			0.433579	−	0.901116i	$-0.357251\pi$
$593$	21.1167			0.867157			0.433579	+	0.901116i	$0.357251\pi$
$594$	0.702183	+	0.268117i	0.0288109	+	0.0110010i
$595$	−1.16608	−	0.237773i	−0.0478044	−	0.00974772i
$596$	17.6812	+	3.75825i	0.724250	+	0.153944i
$597$	−3.85616	−	1.63416i	−0.157822	−	0.0668816i
$598$	1.08228	−	10.2972i	0.0442577	−	0.421084i
$599$	21.7688	+	37.7046i	0.889448	+	1.54057i	0.840529	+	0.541766i	$0.182244\pi$
$599$	21.7688	+	37.7046i	0.889448	+	1.54057i	0.0489185	+	0.998803i	$0.484423\pi$
$600$	6.03947	+	9.67132i	0.246561	+	0.394830i
$601$	13.1713	−	22.8133i	0.537267	−	0.930574i	−0.461783	−	0.886993i	$-0.652790\pi$
$601$	13.1713	−	22.8133i	0.537267	−	0.930574i	0.999050	−	0.0435807i	$-0.0138766\pi$
$602$	0.117568	+	0.0854180i	0.00479171	+	0.00348138i
$603$	−19.2894	−	12.9778i	−0.785525	−	0.528495i
$604$	12.3502	+	38.0099i	0.502521	+	1.54660i
$605$	2.32899	−	24.0770i	0.0946869	−	0.978867i
$606$	−4.91698	+	8.88283i	−0.199739	+	0.360840i
$607$	8.37714	+	14.5096i	0.340018	+	0.588928i	0.984436	−	0.175746i	$-0.0562336\pi$
$607$	8.37714	+	14.5096i	0.340018	+	0.588928i	−0.644418	+	0.764673i	$0.722900\pi$
$608$	−4.78955	+	1.01805i	−0.194242	+	0.0412874i
$609$	−0.923821	+	0.431449i	−0.0374351	+	0.0174832i
$610$	−0.722967	+	7.47399i	−0.0292721	+	0.302613i
$611$	−16.7391	−	12.1617i	−0.677191	−	0.492008i
$612$	6.71955	−	23.5387i	0.271622	−	0.951496i
$613$	−12.7046	+	9.23044i	−0.513134	+	0.372814i	−0.814011	−	0.580849i	$-0.802721\pi$
$613$	−12.7046	+	9.23044i	−0.513134	+	0.372814i	0.300877	+	0.953663i	$0.402721\pi$
$614$	7.44355	−	3.31408i	0.300397	−	0.133746i
$615$	−24.2713	−	4.49459i	−0.978714	−	0.181240i
$616$	0.0631283	+	0.0281065i	0.00254351	+	0.00113244i
$617$	−7.79445	+	1.65676i	−0.313793	+	0.0666987i	−0.362116	−	0.932133i	$-0.617946\pi$
$617$	−7.79445	+	1.65676i	−0.313793	+	0.0666987i	0.0483232	+	0.998832i	$0.484612\pi$
$618$	0.730401	−	0.841233i	0.0293810	−	0.0338393i
$619$	−14.5683	−	16.1797i	−0.585550	−	0.650319i	0.375458	−	0.926839i	$-0.377485\pi$
$619$	−14.5683	−	16.1797i	−0.585550	−	0.650319i	−0.961008	+	0.276520i	$0.910819\pi$
$620$	−3.18180	−	28.0355i	−0.127784	−	1.12593i
$621$	40.0518	−	10.8079i	1.60722	−	0.433706i
$622$	1.78626	+	5.49755i	0.0716227	+	0.220432i
$623$	0.680045	−	0.302776i	0.0272454	−	0.0121305i
$624$	14.4458	−	16.6378i	0.578294	−	0.666045i
$625$	−20.7014	−	14.0161i	−0.828057	−	0.560644i
$626$	1.61402	+	2.79556i	0.0645090	+	0.111733i
$627$	0.280974	−	0.920967i	0.0112210	−	0.0367799i
$628$	42.7130	+	9.07892i	1.70443	+	0.362288i
$629$	8.85131	+	27.2415i	0.352925	+	1.08619i
$630$	−0.0744992	+	0.269412i	−0.00296812	+	0.0107336i
$631$	−5.21668	+	16.0553i	−0.207673	+	0.639151i	0.791920	+	0.610624i	$0.209081\pi$
$631$	−5.21668	+	16.0553i	−0.207673	+	0.639151i	−0.999593	+	0.0285264i	$0.990919\pi$
$632$	−4.24343	+	7.34983i	−0.168794	+	0.292361i
$633$	−3.97721	+	7.18507i	−0.158080	+	0.285581i
$634$	−0.961423	−	0.428053i	−0.0381830	−	0.0170002i
$635$	−3.29656	+	0.0273249i	−0.130820	+	0.00108435i
$636$	13.1853	+	14.1227i	0.522830	+	0.560003i
$637$	2.79413	+	26.5844i	0.110707	+	1.05331i
$638$	−0.560259	+	0.407052i	−0.0221809	+	0.0161153i
$639$	−5.88814	+	11.1056i	−0.232931	+	0.439330i
$640$	−19.0095	+	8.65309i	−0.751417	+	0.342043i
$641$	−0.615338	−	5.85455i	−0.0243044	−	0.231241i	−0.999930	−	0.0118007i	$-0.996244\pi$
$641$	−0.615338	−	5.85455i	−0.0243044	−	0.231241i	0.975626	−	0.219440i	$-0.0704230\pi$
$642$	3.27655	−	0.0591273i	0.129315	−	0.00233357i
$643$	−10.4282	−	18.0622i	−0.411249	−	0.712304i	0.583777	−	0.811914i	$-0.301574\pi$
$643$	−10.4282	−	18.0622i	−0.411249	−	0.712304i	−0.995027	+	0.0996093i	$0.968241\pi$
$644$	1.81017	−	0.384762i	0.0713305	−	0.0151618i
$645$	3.83428	−	12.9516i	0.150975	−	0.509967i
$646$	1.86859	+	0.397180i	0.0735185	+	0.0156268i
$647$	5.43908	+	16.7398i	0.213832	+	0.658108i	0.999234	+	0.0391223i	$0.0124562\pi$
$647$	5.43908	+	16.7398i	0.213832	+	0.658108i	−0.785402	+	0.618986i	$0.787544\pi$
$648$	−11.1444	−	4.02646i	−0.437794	−	0.158174i
$649$	−2.77867			−0.109072
$650$	1.90129	−	6.19942i	0.0745748	−	0.243161i
$651$	0.934598	−	1.07641i	0.0366298	−	0.0421880i
$652$	4.56533	−	43.4362i	0.178792	−	1.70109i
$653$	0.301031	−	0.334329i	0.0117803	−	0.0130833i	−0.737226	−	0.675646i	$-0.763865\pi$
$653$	0.301031	−	0.334329i	0.0117803	−	0.0130833i	0.749006	+	0.662563i	$0.230531\pi$
$654$	−5.97911	+	4.51112i	−0.233802	+	0.176399i
$655$	−28.1287	+	31.7656i	−1.09908	+	1.24119i
$656$	6.54683	−	20.1491i	0.255611	−	0.786689i
$657$	−4.51262	−	31.8362i	−0.176054	−	1.24205i
$658$	−0.0696169	+	0.214259i	−0.00271395	+	0.00835268i
$659$	3.17726	+	30.2296i	0.123769	+	1.17758i	0.863383	+	0.504548i	$0.168341\pi$
$659$	3.17726	+	30.2296i	0.123769	+	1.17758i	−0.739615	+	0.673030i	$0.764992\pi$
$660$	0.244044	−	3.10693i	0.00949941	−	0.120937i
$661$	−3.35305	+	31.9022i	−0.130419	+	1.24085i	0.712059	+	0.702120i	$0.247763\pi$
$661$	−3.35305	+	31.9022i	−0.130419	+	1.24085i	−0.842478	+	0.538731i	$0.818904\pi$
$662$	5.97424	+	2.65990i	0.232196	+	0.103380i
$663$	−25.9953	+	12.1405i	−1.00957	+	0.471497i
$664$	3.12514	−	1.39140i	0.121279	−	0.0539969i
$665$	0.350862	+	0.0715438i	0.0136059	+	0.00277435i
$666$	6.52599	−	1.63530i	0.252877	−	0.0633665i
$667$	−11.8112	+	36.3512i	−0.457332	+	1.40752i
$668$	−23.8425	+	41.2964i	−0.922492	+	1.59780i
$669$	−22.9948	+	0.414955i	−0.889031	+	0.0160431i
$670$	1.76830	−	5.59978i	0.0683154	−	0.216338i
$671$	2.83026	−	3.14332i	0.109261	−	0.121347i
$672$	−0.737247	−	0.312429i	−0.0284399	−	0.0120522i
$673$	25.1007	−	11.1756i	0.967561	−	0.430786i	0.138758	−	0.990326i	$-0.455689\pi$
$673$	25.1007	−	11.1756i	0.967561	−	0.430786i	0.828803	+	0.559540i	$0.189022\pi$
$674$	−2.15922			−0.0831700
$675$	25.9158	−	1.83552i	0.997501	−	0.0706494i
$676$	−3.10212			−0.119312
$677$	−31.4534	+	14.0040i	−1.20885	+	0.538216i	−0.909411	−	0.415899i	$-0.863467\pi$
$677$	−31.4534	+	14.0040i	−1.20885	+	0.538216i	−0.299441	+	0.954115i	$0.596800\pi$
$678$	0.359019	+	0.152144i	0.0137880	+	0.00584307i
$679$	−1.14984	+	1.27702i	−0.0441266	+	0.0490076i
$680$	12.7424	−	0.105621i	0.488650	−	0.00405037i
$681$	6.75681	−	0.121931i	0.258921	−	0.00467239i
$682$	0.484112	−	0.838507i	0.0185376	−	0.0321081i
$683$	−5.56214	+	17.1185i	−0.212830	+	0.655022i	0.786471	+	0.617627i	$0.211906\pi$
$683$	−5.56214	+	17.1185i	−0.212830	+	0.655022i	−0.999301	+	0.0373948i	$0.988094\pi$
$684$	−2.02186	+	7.08260i	−0.0773076	+	0.270810i
$685$	7.12363	+	7.78091i	0.272180	+	0.297293i
$686$	0.532353	−	0.237019i	0.0203254	−	0.00904943i
$687$	28.6180	−	13.3654i	1.09185	−	0.509921i
$688$	10.5908	+	4.71533i	0.403771	+	0.179770i
$689$	2.36706	−	22.5211i	0.0901778	−	0.857985i
$690$	5.47634	+	8.93352i	0.208481	+	0.340093i
$691$	3.98177	+	37.8840i	0.151474	+	1.44118i	0.761176	+	0.648546i	$0.224623\pi$
$691$	3.98177	+	37.8840i	0.151474	+	1.44118i	−0.609702	+	0.792631i	$0.708711\pi$
$692$	−0.588284	+	1.81055i	−0.0223632	+	0.0688269i
$693$	0.123962	−	0.0970856i	0.00470893	−	0.00368798i
$694$	−3.00544	+	9.24980i	−0.114085	+	0.351118i
$695$	17.9073	+	30.4310i	0.679262	+	1.15431i
$696$	8.71529	−	6.57551i	0.330352	−	0.249244i
$697$	−18.4589	+	20.5006i	−0.699179	+	0.776517i
$698$	0.387824	−	3.68990i	0.0146793	−	0.139665i
$699$	−20.6827	+	23.8211i	−0.782291	+	0.900996i
$700$	1.15883	−	0.0192122i	0.0437998	−	0.000726154i
$701$	−41.5141			−1.56797			−0.783983	−	0.620783i	$-0.786815\pi$
$701$	−41.5141			−1.56797			−0.783983	+	0.620783i	$0.786815\pi$
$702$	2.42611	+	6.28693i	0.0915677	+	0.237285i
$703$	−2.66329	−	8.19675i	−0.100448	−	0.309146i
$704$	2.24383	+	0.476942i	0.0845677	+	0.0179754i
$705$	20.9323	−	0.551323i	0.788355	−	0.0207640i
$706$	0.720758	−	0.153202i	0.0271261	−	0.00576583i
$707$	1.06344	+	1.84193i	0.0399948	+	0.0692730i
$708$	21.2521	−	0.383506i	0.798703	−	0.0144131i
$709$	−1.28050	−	12.1831i	−0.0480902	−	0.457547i	−0.991897	−	0.127048i	$-0.959450\pi$
$709$	−1.28050	−	12.1831i	−0.0480902	−	0.457547i	0.943806	−	0.330499i	$-0.107217\pi$
$710$	−3.11101	−	0.634360i	−0.116754	−	0.0238071i
$711$	10.2669	+	16.3874i	0.385039	+	0.614576i
$712$	−6.44852	+	4.68512i	−0.241669	+	0.175582i
$713$	−5.58588	−	53.1461i	−0.209193	−	1.99034i
$714$	0.213184	+	0.228342i	0.00797821	+	0.00854547i
$715$	−2.93718	+	2.17141i	−0.109844	+	0.0812061i
$716$	−0.907574	−	0.404078i	−0.0339176	−	0.0151011i
$717$	6.03014	−	10.8938i	0.225200	−	0.406837i
$718$	3.58822	−	6.21499i	0.133911	−	0.231941i
$719$	13.9757	−	43.0129i	0.521207	−	1.60411i	−0.250489	−	0.968119i	$-0.580591\pi$
$719$	13.9757	−	43.0129i	0.521207	−	1.60411i	0.771696	−	0.635991i	$-0.219409\pi$
$720$	−1.34479	+	22.2584i	−0.0501174	+	0.829523i
$721$	−0.0721189	−	0.221959i	−0.00268585	−	0.00826619i
$722$	5.73581	+	1.21918i	0.213465	+	0.0453734i
$723$	9.98354	−	32.7238i	0.371292	−	1.21701i
$724$	−12.2726	−	21.2567i	−0.456107	−	0.790001i
$725$	−11.6235	+	20.9260i	−0.431685	+	0.777173i
$726$	−4.16290	+	4.79458i	−0.154500	+	0.177944i
$727$	35.4050	−	15.7633i	1.31310	−	0.584628i	0.373729	−	0.927538i	$-0.378079\pi$
$727$	35.4050	−	15.7633i	1.31310	−	0.584628i	0.939368	+	0.342910i	$0.111412\pi$
$728$	0.191450	+	0.589222i	0.00709560	+	0.0218380i
$729$	−20.0008	+	18.1375i	−0.740770	+	0.671759i
$730$	7.39200	−	3.36482i	0.273590	−	0.124538i
$731$	−10.1008	−	11.2181i	−0.373591	−	0.414915i
$732$	−21.2128	+	24.4316i	−0.784047	+	0.903019i
$733$	−17.7677	+	3.77663i	−0.656263	+	0.139493i	−0.523996	−	0.851721i	$-0.675559\pi$
$733$	−17.7677	+	3.77663i	−0.656263	+	0.139493i	−0.132268	+	0.991214i	$0.542226\pi$
$734$	5.36632	+	2.38924i	0.198074	+	0.0881884i
$735$	−18.6246	−	19.6202i	−0.686978	−	0.723703i
$736$	−27.4213	+	12.2088i	−1.01076	+	0.450021i
$737$	−2.67614	+	1.94433i	−0.0985770	+	0.0716204i
$738$	4.50651	+	4.65562i	0.165887	+	0.171376i
$739$	12.8872	+	9.36310i	0.474063	+	0.344427i	0.799023	−	0.601301i	$-0.205351\pi$
$739$	12.8872	+	9.36310i	0.474063	+	0.344427i	−0.324960	+	0.945728i	$0.605351\pi$
$740$	−14.1475	−	24.0417i	−0.520072	−	0.883792i
$741$	7.82176	−	3.65297i	0.287340	−	0.134195i
$742$	−0.241178	+	0.0512640i	−0.00885392	+	0.00188196i
$743$	4.11285	+	7.12366i	0.150886	+	0.261342i	0.931553	−	0.363605i	$-0.118454\pi$
$743$	4.11285	+	7.12366i	0.150886	+	0.261342i	−0.780668	+	0.624947i	$0.785121\pi$
$744$	−7.39231	+	13.3547i	−0.271015	+	0.489606i
$745$	19.6589	+	8.55817i	0.720246	+	0.313547i
$746$	2.46707	+	7.59287i	0.0903259	+	0.277995i
$747$	0.534555	−	7.77642i	0.0195583	−	0.284524i
$748$	−2.81776	−	2.04722i	−0.103028	−	0.0748539i
$749$	0.343250	−	0.594527i	0.0125421	−	0.0217236i
$750$	2.29376	+	6.14850i	0.0837563	+	0.224511i
$751$	14.9771	+	25.9412i	0.546523	+	0.946606i	0.998509	+	0.0545813i	$0.0173824\pi$
$751$	14.9771	+	25.9412i	0.546523	+	0.946606i	−0.451986	+	0.892025i	$0.649284\pi$
$752$	−1.87861	+	17.8737i	−0.0685057	+	0.651788i
$753$	−31.1049	−	13.1816i	−1.13352	−	0.480363i
$754$	−6.07316	−	1.29089i	−0.221171	−	0.0470114i
$755$	5.34581	+	47.1029i	0.194554	+	1.71425i
$756$	−0.934698	+	0.759648i	−0.0339946	+	0.0276281i
$757$	−28.4622			−1.03448			−0.517238	−	0.855841i	$-0.673040\pi$
$757$	−28.4622			−1.03448			−0.517238	+	0.855841i	$0.673040\pi$
$758$	2.50638	+	2.78362i	0.0910359	+	0.101106i
$759$	0.510967	−	5.88036i	0.0185469	−	0.213444i
$760$	−3.83409	+	0.0317804i	−0.139077	+	0.00115280i
$761$	0.762237	−	7.25220i	0.0276311	−	0.262892i	−0.971981	−	0.235057i	$-0.924472\pi$
$761$	0.762237	−	7.25220i	0.0276311	−	0.262892i	0.999613	−	0.0278345i	$-0.00886114\pi$
$762$	0.709160	+	0.495936i	0.0256902	+	0.0179659i
$763$	0.164010	+	1.56045i	0.00593755	+	0.0564920i
$764$	14.4705	+	10.5134i	0.523523	+	0.380361i
$765$	13.3880	−	25.7649i	0.484045	−	0.931531i
$766$	−3.61078	+	2.62338i	−0.130463	+	0.0947867i
$767$	−16.6697	−	18.5136i	−0.601908	−	0.668486i
$768$	−12.8943	−	2.49850i	−0.465283	−	0.0901568i
$769$	35.7136	−	7.59117i	1.28787	−	0.273744i	0.487430	−	0.873162i	$-0.337934\pi$
$769$	35.7136	−	7.59117i	1.28787	−	0.273744i	0.800436	+	0.599418i	$0.204601\pi$
$770$	0.0323683	+	0.0231095i	0.00116647	+	0.000832808i
$771$	−2.01226	−	16.3089i	−0.0724697	−	0.587351i
$772$	−11.6301	−	2.47206i	−0.418577	−	0.0889713i
$773$	34.7818	+	25.2705i	1.25102	+	0.908916i	0.998280	−	0.0586197i	$-0.0186699\pi$
$773$	34.7818	+	25.2705i	1.25102	+	0.908916i	0.252735	+	0.967536i	$0.418670\pi$
$774$	−2.79139	+	2.18618i	−0.100334	+	0.0785808i
$775$	2.94609	−	33.3376i	0.105827	−	1.19752i
$776$	9.20003	−	15.9349i	0.330262	−	0.572031i
$777$	0.411263	−	1.34803i	0.0147540	−	0.0483602i
$778$	−0.449731	+	0.499477i	−0.0161236	+	0.0179071i
$779$	5.55412	−	6.16848i	0.198997	−	0.221009i
$780$	22.1647	−	17.0130i	0.793624	−	0.609162i
$781$	1.19673	+	1.32911i	0.0428225	+	0.0475592i
$782$	11.7105			0.418768
$783$	−3.93506	−	24.5634i	−0.140628	−	0.877823i
$784$	18.7844	−	13.6476i	0.670870	−	0.487415i
$785$	47.4906	+	20.6742i	1.69501	+	0.737894i
$786$	10.8507	−	2.51183i	0.387032	−	0.0895942i
$787$	−25.7664	−	11.4720i	−0.918474	−	0.408931i	−0.107628	−	0.994191i	$-0.534326\pi$
$787$	−25.7664	−	11.4720i	−0.918474	−	0.408931i	−0.810846	+	0.585260i	$0.800992\pi$
$788$	41.1164	+	18.3062i	1.46471	+	0.652132i
$789$	7.69491	−	25.2221i	0.273946	−	0.897932i
$790$	−3.23819	+	3.65688i	−0.115210	+	0.130106i
$791$	0.0660835	−	0.0480125i	0.00234966	−	0.00170713i
$792$	−1.08220	+	1.29281i	−0.0384543	+	0.0459381i
$793$	37.9223			1.34666
$794$	1.71028	+	1.89946i	0.0606955	+	0.0674091i
$795$	11.9774	+	19.5386i	0.424793	+	0.692962i
$796$	3.05013	−	3.38752i	0.108109	−	0.120067i
$797$	−6.65667	+	7.39298i	−0.235791	+	0.261873i	−0.849415	−	0.527726i	$-0.823045\pi$
$797$	−6.65667	+	7.39298i	−0.235791	+	0.261873i	0.613623	+	0.789599i	$0.289711\pi$
$798$	−0.0641453	−	0.0687061i	−0.00227072	−	0.00243217i
$799$	11.7008	−	20.2664i	0.413945	−	0.716974i
$800$	−18.3205	+	4.21271i	−0.647726	+	0.148942i
$801$	2.54891	+	17.9824i	0.0900613	+	0.635375i
$802$	−6.82139	−	4.95603i	−0.240871	−	0.175003i
$803$	−4.47504	−	0.951199i	−0.157921	−	0.0335671i
$804$	20.1996	−	15.2402i	0.712383	−	0.537479i
$805$	2.19501	−	0.0181942i	0.0773638	−	0.000641261i
$806$	8.49101	−	1.80482i	0.299083	−	0.0635721i
$807$	−29.6453	+	34.1437i	−1.04356	+	1.20192i
$808$	−15.2387	−	16.9243i	−0.536097	−	0.595396i
$809$	−25.8548	+	18.7846i	−0.909008	+	0.660433i	−0.940764	−	0.339063i	$-0.889890\pi$
$809$	−25.8548	+	18.7846i	−0.909008	+	0.660433i	0.0317559	+	0.999496i	$0.489890\pi$
$810$	−5.82174	−	3.55218i	−0.204555	−	0.124811i
$811$	−18.9233	−	13.7486i	−0.664488	−	0.482779i	0.203687	−	0.979036i	$-0.434707\pi$
$811$	−18.9233	−	13.7486i	−0.664488	−	0.482779i	−0.868176	+	0.496257i	$0.834707\pi$
$812$	−0.115999	−	1.10366i	−0.00407076	−	0.0387307i
$813$	1.96788	−	22.6470i	0.0690167	−	0.794265i
$814$	0.100059	−	0.952000i	0.00350707	−	0.0333676i
$815$	15.5998	−	49.4008i	0.546437	−	1.73043i
$816$	20.4225	+	14.2820i	0.714931	+	0.499971i
$817$	3.03925	+	3.37542i	0.106330	+	0.118091i
$818$	−0.261828			−0.00915459
$819$	1.39052	+	0.243494i	0.0485888	+	0.00850838i
$820$	13.2397	−	23.3771i	0.462349	−	0.816365i
$821$	−17.2322	−	3.66282i	−0.601409	−	0.127833i	−0.102861	−	0.994696i	$-0.532800\pi$
$821$	−17.2322	−	3.66282i	−0.601409	−	0.127833i	−0.498548	+	0.866862i	$0.666133\pi$
$822$	−0.339100	−	2.74833i	−0.0118275	−	0.0958590i
$823$	1.04962	−	9.98642i	0.0365873	−	0.348105i	−0.960879	−	0.276968i	$-0.910671\pi$
$823$	1.04962	−	9.98642i	0.0365873	−	0.348105i	0.997467	−	0.0711371i	$-0.0226628\pi$
$824$	1.24949	+	2.16417i	0.0435279	+	0.0753926i
$825$	1.01994	−	3.55312i	0.0355098	−	0.123704i
$826$	−0.135627	+	0.234912i	−0.00471905	+	0.00817364i
$827$	15.6072	+	11.3393i	0.542717	+	0.394307i	0.825093	−	0.564997i	$-0.191123\pi$
$827$	15.6072	+	11.3393i	0.542717	+	0.394307i	−0.282376	+	0.959304i	$0.591123\pi$
$828$	−3.09643	+	45.0452i	−0.107608	+	1.56543i
$829$	−13.6525	−	42.0179i	−0.474170	−	1.45934i	−0.847075	−	0.531474i	$-0.821638\pi$
$829$	−13.6525	−	42.0179i	−0.474170	−	1.45934i	0.372905	−	0.927870i	$-0.378362\pi$
$830$	1.92238	−	0.425298i	0.0667268	−	0.0147623i
$831$	−43.3733	+	0.782696i	−1.50460	+	0.0271514i
$832$	10.2834	+	17.8113i	0.356512	+	0.617496i
$833$	−29.5725	+	6.28583i	−1.02463	+	0.217791i
$834$	0.802350	−	9.23368i	0.0277831	−	0.319736i
$835$	−37.4971	+	42.3454i	−1.29764	+	1.46542i
$836$	0.847841	+	0.615993i	0.0293232	+	0.0213046i
$837$	18.9944	+	29.1358i	0.656544	+	1.00708i
$838$	4.45507	−	3.23680i	0.153898	−	0.111813i
$839$	6.84736	−	3.04864i	0.236397	−	0.105251i	−0.285119	−	0.958492i	$-0.592033\pi$
$839$	6.84736	−	3.04864i	0.236397	−	0.105251i	0.521516	+	0.853241i	$0.325367\pi$
$840$	−0.516779	−	0.355056i	−0.0178306	−	0.0122506i
$841$	−5.55422	−	2.47290i	−0.191525	−	0.0852724i
$842$	−11.7160	+	2.49032i	−0.403760	+	0.0858219i
$843$	4.56782	+	13.2405i	0.157324	+	0.456028i
$844$	−5.98092	−	6.64249i	−0.205872	−	0.228644i
$845$	−3.60536	−	0.735164i	−0.124028	−	0.0252904i
$846$	−4.56048	−	3.06826i	−0.156793	−	0.105489i
$847$	0.411040	+	1.26505i	0.0141235	+	0.0434677i
$848$	−17.9693	+	8.00046i	−0.617069	+	0.274737i
$849$	−13.6537	−	2.64565i	−0.468595	−	0.0907986i
$850$	7.19807	+	1.40571i	0.246892	+	0.0482153i
$851$	−26.4164	−	45.7545i	−0.905542	−	1.56845i
$852$	−9.33641	−	10.0002i	−0.319860	−	0.342602i
$853$	−0.382686	−	0.0813423i	−0.0131029	−	0.00278511i	0.201356	−	0.979518i	$-0.435465\pi$
$853$	−0.382686	−	0.0813423i	−0.0131029	−	0.00278511i	−0.214458	+	0.976733i	$0.568799\pi$
$854$	−0.127595	−	0.392698i	−0.00436622	−	0.0134379i
$855$	−4.02835	+	7.75244i	−0.137767	+	0.265128i
$856$	−2.27153	+	6.99105i	−0.0776393	+	0.238949i
$857$	−9.45377	+	16.3744i	−0.322935	+	0.559339i	−0.981092	−	0.193541i	$-0.938003\pi$
$857$	−9.45377	+	16.3744i	−0.322935	+	0.559339i	0.658158	+	0.752880i	$0.271336\pi$
$858$	0.958661	−	0.0172996i	0.0327281	−	0.000590598i
$859$	−17.7444	−	7.90030i	−0.605430	−	0.269555i	0.0810426	−	0.996711i	$-0.474175\pi$
$859$	−17.7444	−	7.90030i	−0.605430	−	0.269555i	−0.686472	+	0.727156i	$0.740842\pi$
$860$	11.9647	+	8.54227i	0.407994	+	0.291289i
$861$	1.32238	−	0.306118i	0.0450667	−	0.0104325i
$862$	−0.859522	−	8.17780i	−0.0292754	−	0.278537i
$863$	13.1723	−	9.57020i	0.448389	−	0.325773i	−0.340571	−	0.940219i	$-0.610620\pi$
$863$	13.1723	−	9.57020i	0.448389	−	0.325773i	0.788959	+	0.614446i	$0.210620\pi$
$864$	12.2675	−	15.2041i	0.417350	−	0.517254i
$865$	−1.11280	+	1.96486i	−0.0378363	+	0.0668071i
$866$	−0.626830	−	5.96389i	−0.0213005	−	0.202661i
$867$	−1.54912	−	2.57472i	−0.0526108	−	0.0874421i
$868$	0.775773	+	1.34368i	0.0263314	+	0.0456074i
$869$	2.69133	−	0.572060i	0.0912972	−	0.0194058i
$870$	5.67100	−	2.70599i	0.192265	−	0.0917416i
$871$	−29.0092	−	6.16609i	−0.982938	−	0.208930i
$872$	−5.19173	−	15.9785i	−0.175814	−	0.541100i
$873$	−22.2594	−	35.5290i	−0.753365	−	1.20247i
$874$	−3.52360			−0.119188
$875$	1.35138	+	0.252300i	0.0456850	+	0.00852931i
$876$	34.3577	+	6.65741i	1.16084	+	0.224933i
$877$	0.619227	−	5.89155i	0.0209098	−	0.198944i	−0.979080	−	0.203476i	$-0.934776\pi$
$877$	0.619227	−	5.89155i	0.0209098	−	0.198944i	0.999990	+	0.00453249i	$0.00144274\pi$
$878$	−5.17074	+	5.74269i	−0.174504	+	0.193806i
$879$	−2.58360	−	20.9395i	−0.0871427	−	0.706273i
$880$	2.90906	+	1.26641i	0.0980645	+	0.0426907i
$881$	10.8019	−	33.2448i	0.363925	−	1.12005i	−0.586727	−	0.809785i	$-0.699584\pi$
$881$	10.8019	−	33.2448i	0.363925	−	1.12005i	0.950652	−	0.310260i	$-0.100416\pi$
$882$	0.996591	+	7.03087i	0.0335570	+	0.236742i
$883$	−4.71649	+	14.5159i	−0.158723	+	0.488498i	−0.998519	−	0.0544035i	$-0.982674\pi$
$883$	−4.71649	+	14.5159i	−0.158723	+	0.488498i	0.839796	+	0.542901i	$0.182674\pi$
$884$	−3.26408	−	31.0556i	−0.109783	−	1.04451i
$885$	24.7906	+	4.59077i	0.833328	+	0.154317i
$886$	0.206350	−	1.96329i	0.00693245	−	0.0659579i
$887$	−2.21677	−	0.986968i	−0.0744317	−	0.0331391i	0.369183	−	0.929357i	$-0.379638\pi$
$887$	−2.21677	−	0.986968i	−0.0744317	−	0.0331391i	−0.443615	+	0.896218i	$0.646304\pi$
$888$	−1.30639	+	15.0344i	−0.0438397	+	0.504520i
$889$	0.165609	−	0.0737339i	0.00555435	−	0.00247296i
$890$	−4.17530	+	1.90059i	−0.139957	+	0.0637079i
$891$	1.44751	+	3.55849i	0.0484934	+	0.119214i
$892$	7.73518	−	23.8064i	0.258993	−	0.797098i
$893$	−3.52068	+	6.09800i	−0.117815	+	0.204062i
$894$	−2.90158	−	4.82258i	−0.0970432	−	0.161291i
$895$	−0.959045	−	0.684714i	−0.0320574	−	0.0228875i
$896$	0.768511	−	0.853518i	0.0256742	−	0.0285140i
$897$	42.2447	−	31.8728i	1.41051	−	1.06420i
$898$	−1.09329	+	0.486765i	−0.0364836	+	0.0162435i
$899$	−32.0452			−1.06877
$900$	−7.31040	+	27.3161i	−0.243680	+	0.910536i
$901$	25.6122			0.853266
$902$	0.842212	−	0.374977i	0.0280426	−	0.0124854i
$903$	0.0909537	+	0.737160i	0.00302675	+	0.0245312i
$904$	−0.585250	+	0.649986i	−0.0194651	+	0.0216182i
$905$	−9.22594	−	27.6136i	−0.306681	−	0.917908i
$906$	6.02642	−	10.8871i	0.200214	−	0.361700i
$907$	−23.7505	+	41.1370i	−0.788621	+	1.36593i	0.138191	+	0.990406i	$0.455871\pi$
$907$	−23.7505	+	41.1370i	−0.788621	+	1.36593i	−0.926812	+	0.375526i	$0.877462\pi$
$908$	−2.27291	+	6.99529i	−0.0754291	+	0.232147i
$909$	−50.3359	+	12.6133i	−1.66954	+	0.418357i
$910$	0.0402101	+	0.354299i	0.00133295	+	0.0117449i
$911$	−36.3002	+	16.1619i	−1.20268	+	0.535468i	−0.907532	−	0.419983i	$-0.862036\pi$
$911$	−36.3002	+	16.1619i	−1.20268	+	0.535468i	−0.295149	+	0.955451i	$0.595369\pi$
$912$	−6.14496	−	4.29735i	−0.203480	−	0.142299i
$913$	−1.01318	−	0.451096i	−0.0335313	−	0.0149291i
$914$	0.113944	−	1.08410i	0.00376893	−	0.0358589i
$915$	−30.4441	+	23.3679i	−1.00645	+	0.772520i
$916$	3.59340	+	34.1889i	0.118729	+	1.12963i
$917$	0.720991	−	2.21898i	0.0238092	−	0.0732772i
$918$	−6.78490	+	3.47223i	−0.223935	+	0.114601i
$919$	17.4265	−	53.6333i	0.574847	−	1.76920i	−0.0618513	−	0.998085i	$-0.519700\pi$
$919$	17.4265	−	53.6333i	0.574847	−	1.76920i	0.636699	−	0.771113i	$-0.280300\pi$
$920$	−22.9493	+	5.07719i	−0.756616	+	0.167390i
$921$	38.3440	+	16.2493i	1.26348	+	0.535434i
$922$	3.62200	−	4.02264i	0.119284	−	0.132479i
$923$	−1.67610	+	15.9471i	−0.0551696	+	0.524904i
$924$	0.0558896	+	0.162004i	0.00183863	+	0.00532955i
$925$	−10.7450	−	31.2947i	−0.353293	−	1.02896i
$926$	−4.36273			−0.143368
$927$	5.69040	−	0.205440i	0.186897	−	0.00674754i
$928$	5.56219	+	17.1187i	0.182588	+	0.561948i
$929$	23.5805	+	5.01219i	0.773650	+	0.164444i	0.577788	−	0.816187i	$-0.303916\pi$
$929$	23.5805	+	5.01219i	0.773650	+	0.164444i	0.195862	+	0.980631i	$0.437249\pi$
$930$	−5.70447	+	6.68113i	−0.187057	+	0.219083i
$931$	8.89813	−	1.89136i	0.291624	−	0.0619867i
$932$	−17.1679	−	29.7356i	−0.562352	−	0.974023i
$933$	−14.3082	+	25.8486i	−0.468428	+	0.846244i
$934$	0.358248	+	3.40850i	0.0117222	+	0.111529i
$935$	−2.78971	−	3.04711i	−0.0912333	−	0.0996513i
$936$	−15.1060	+	0.545370i	−0.493754	+	0.0178260i
$937$	38.4141	−	27.9095i	1.25493	−	0.911764i	0.256437	−	0.966561i	$-0.417451\pi$
$937$	38.4141	−	27.9095i	1.25493	−	0.911764i	0.998498	+	0.0547973i	$0.0174513\pi$
$938$	0.0337539	+	0.321147i	0.00110210	+	0.0104858i
$939$	−4.81444	+	15.7806i	−0.157113	+	0.514982i
$940$	−6.86276	+	21.7327i	−0.223839	+	0.708843i
$941$	−14.3492	−	6.38867i	−0.467770	−	0.208265i	0.159296	−	0.987231i	$-0.449078\pi$
$941$	−14.3492	−	6.38867i	−0.467770	−	0.208265i	−0.627066	+	0.778966i	$0.715744\pi$
$942$	−7.00942	−	11.6501i	−0.228379	−	0.379579i
$943$	25.4415	−	44.0659i	0.828488	−	1.43498i
$944$	−6.68691	+	20.5802i	−0.217641	+	0.669829i
$945$	−1.26636	+	0.661371i	−0.0411946	+	0.0215144i
$946$	0.155892	+	0.479787i	0.00506849	+	0.0155992i
$947$	2.69215	+	0.572234i	0.0874831	+	0.0185951i	0.251445	−	0.967872i	$-0.419094\pi$
$947$	2.69215	+	0.572234i	0.0874831	+	0.0185951i	−0.163962	+	0.986467i	$0.552427\pi$
$948$	−20.5051	+	4.74673i	−0.665976	+	0.154167i
$949$	−20.5089	−	35.5224i	−0.665746	−	1.15311i
$950$	−2.16584	−	0.422966i	−0.0702691	−	0.0137228i
$951$	−1.75421	−	5.08485i	−0.0568842	−	0.164888i
$952$	−0.640140	+	0.285009i	−0.0207471	+	0.00923719i
$953$	−3.45530	−	10.6343i	−0.111928	−	0.344479i	0.879366	−	0.476147i	$-0.157967\pi$
$953$	−3.45530	−	10.6343i	−0.111928	−	0.344479i	−0.991294	+	0.131667i	$0.957967\pi$
$954$	0.412554	−	6.00162i	0.0133569	−	0.194309i
$955$	14.3264	+	15.6483i	0.463592	+	0.506366i
$956$	9.06812	+	10.0712i	0.293284	+	0.325725i
$957$	−3.47488	−	0.673319i	−0.112327	−	0.0217653i
$958$	4.16054	−	0.884351i	0.134421	−	0.0285721i
$959$	−0.529948	−	0.235948i	−0.0171129	−	0.00761916i
$960$	−19.2310	−	7.96229i	−0.620677	−	0.256982i
$961$	12.6097	−	5.61421i	0.406765	−	0.181104i
$962$	6.94319	−	5.04453i	0.223858	−	0.162642i
$963$	11.6493	+	12.0348i	0.375395	+	0.387815i
$964$	30.1254	+	21.8874i	0.970275	+	0.704946i
$965$	−12.9310	−	5.62929i	−0.416263	−	0.181213i
$966$	−0.472192	−	0.330217i	−0.0151925	−	0.0106246i
$967$	11.5960	−	2.46480i	0.372901	−	0.0792625i	−0.0176491	−	0.999844i	$-0.505618\pi$
$967$	11.5960	−	2.46480i	0.372901	−	0.0792625i	0.390550	+	0.920582i	$0.372285\pi$
$968$	−7.12142	−	12.3347i	−0.228891	−	0.396451i
$969$	5.03369	+	8.36628i	0.161705	+	0.268764i
$970$	7.02061	−	7.92836i	0.225418	−	0.254564i
$971$	8.31541	+	25.5922i	0.266854	+	0.821293i	0.991260	+	0.131919i	$0.0421140\pi$
$971$	8.31541	+	25.5922i	0.266854	+	0.821293i	−0.724406	+	0.689373i	$0.757886\pi$
$972$	−11.5621	−	27.0166i	−0.370855	−	0.866558i
$973$	−1.57079	−	1.14125i	−0.0503574	−	0.0365868i
$974$	−2.37217	+	4.10872i	−0.0760092	+	0.131652i
$975$	29.7923	−	14.5201i	0.954117	−	0.465017i
$976$	−16.4699	−	28.5267i	−0.527189	−	0.913118i
$977$	6.04142	−	57.4802i	0.193282	−	1.83896i	−0.282350	−	0.959311i	$-0.591114\pi$
$977$	6.04142	−	57.4802i	0.193282	−	1.83896i	0.475632	−	0.879644i	$-0.342219\pi$
$978$	−10.8556	+	8.19034i	−0.347124	+	0.261898i
$979$	2.52769	+	0.537276i	0.0807852	+	0.0171714i
$980$	26.7979	−	12.1984i	0.856029	−	0.389662i
$981$	−37.7081	−	6.60306i	−1.20393	−	0.210820i
$982$	7.83620			0.250063
$983$	−14.7479	−	16.3792i	−0.470386	−	0.522417i	0.460533	−	0.887643i	$-0.347658\pi$
$983$	−14.7479	−	16.3792i	−0.470386	−	0.522417i	−0.930919	+	0.365226i	$0.880992\pi$
$984$	−13.1687	+	6.15014i	−0.419803	+	0.196059i
$985$	43.4483	+	31.0201i	1.38438	+	0.988382i
$986$	0.734035	−	6.98388i	0.0233764	−	0.222412i
$987$	−1.04328	+	0.487239i	−0.0332080	+	0.0155090i
$988$	0.982134	+	9.34438i	0.0312458	+	0.297284i
$989$	22.5258	+	16.3660i	0.716279	+	0.520407i
$990$	−0.758955	+	0.604621i	−0.0241212	+	0.0192161i
$991$	1.39340	−	1.01236i	0.0442627	−	0.0321588i	−0.565434	−	0.824794i	$-0.691291\pi$
$991$	1.39340	−	1.01236i	0.0442627	−	0.0321588i	0.609697	+	0.792635i	$0.291291\pi$
$992$	−16.8391	−	18.7017i	−0.534643	−	0.593781i
$993$	10.9006	+	31.5971i	0.345920	+	1.00270i
$994$	0.170777	−	0.0362997i	0.00541671	−	0.00115136i
$995$	4.34775	−	3.21422i	0.137833	−	0.101898i
$996$	7.81134	+	3.31028i	0.247512	+	0.104890i
$997$	32.5749	+	6.92401i	1.03166	+	0.219286i	0.692480	−	0.721437i	$-0.256518\pi$
$997$	32.5749	+	6.92401i	1.03166	+	0.219286i	0.339178	+	0.940722i	$0.389851\pi$
$998$	6.62635	+	4.81433i	0.209753	+	0.152395i
$999$	28.8717	+	18.6769i	0.913460	+	0.590910i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.q.a.16.16	✓	224
3.2	odd	2		675.2.r.a.316.13		224
9.4	even	3	inner	225.2.q.a.166.13	yes	224
9.5	odd	6		675.2.r.a.91.16		224
25.11	even	5	inner	225.2.q.a.61.13	yes	224
75.11	odd	10		675.2.r.a.586.16		224
225.86	odd	30		675.2.r.a.361.13		224
225.211	even	15	inner	225.2.q.a.211.16	yes	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.16.16	✓	224	1.1	even	1	trivial
225.2.q.a.61.13	yes	224	25.11	even	5	inner
225.2.q.a.166.13	yes	224	9.4	even	3	inner
225.2.q.a.211.16	yes	224	225.211	even	15	inner
675.2.r.a.91.16		224	9.5	odd	6
675.2.r.a.316.13		224	3.2	odd	2
675.2.r.a.361.13		224	225.86	odd	30
675.2.r.a.586.16		224	75.11	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.q (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309584 - 0.137836i) q^{2} +(1.59476 + 0.675825i) q^{3} +(-1.26142 + 1.40095i) q^{4} +(-1.79806 + 1.32928i) q^{5} +(0.586865 - 0.0105903i) q^{6} +(0.0614798 - 0.106486i) q^{7} +(-0.406855 + 1.25217i) q^{8} +(2.08652 + 2.15556i) q^{9} +O(q^{10})\)	\(q+(0.309584 - 0.137836i) q^{2} +(1.59476 + 0.675825i) q^{3} +(-1.26142 + 1.40095i) q^{4} +(-1.79806 + 1.32928i) q^{5} +(0.586865 - 0.0105903i) q^{6} +(0.0614798 - 0.106486i) q^{7} +(-0.406855 + 1.25217i) q^{8} +(2.08652 + 2.15556i) q^{9} +(-0.373429 + 0.659360i) q^{10} +(0.389945 - 0.173615i) q^{11} +(-2.95845 + 1.38168i) q^{12} +(3.49609 + 1.55656i) q^{13} +(0.00435558 - 0.0414406i) q^{14} +(-3.76583 + 0.904704i) q^{15} +(-0.347467 - 3.30593i) q^{16} +(-1.33754 + 4.11653i) q^{17} +(0.943067 + 0.379729i) q^{18} +(0.402455 - 1.23863i) q^{19} +(0.405860 - 4.19576i) q^{20} +(0.170012 - 0.128270i) q^{21} +(0.0967906 - 0.107497i) q^{22} +(0.834522 - 7.93995i) q^{23} +(-1.49508 + 1.72195i) q^{24} +(1.46605 - 4.78024i) q^{25} +1.29688 q^{26} +(1.87072 + 4.84772i) q^{27} +(0.0716297 + 0.220453i) q^{28} +(-4.68288 - 0.995377i) q^{29} +(-1.04114 + 0.799149i) q^{30} +(6.54724 - 1.39166i) q^{31} +(-1.87986 - 3.25601i) q^{32} +(0.739203 - 0.0133393i) q^{33} +(0.153323 + 1.45877i) q^{34} +(0.0310051 + 0.273192i) q^{35} +(-5.65179 + 0.204046i) q^{36} +(5.35375 - 3.88973i) q^{37} +(-0.0461337 - 0.438933i) q^{38} +(4.52347 + 4.84509i) q^{39} +(-0.932932 - 2.79230i) q^{40} +(5.82236 + 2.59228i) q^{41} +(0.0349527 - 0.0631441i) q^{42} +(-1.74377 + 3.02030i) q^{43} +(-0.248659 + 0.765293i) q^{44} +(-6.61703 - 1.10226i) q^{45} +(-0.836054 - 2.57311i) q^{46} +(-5.28842 - 1.12409i) q^{47} +(1.68010 - 5.50700i) q^{48} +(3.49244 + 6.04908i) q^{49} +(-0.205024 - 1.68196i) q^{50} +(-4.91511 + 5.66093i) q^{51} +(-6.59069 + 2.93436i) q^{52} +(-1.82854 - 5.62767i) q^{53} +(1.24734 + 1.24293i) q^{54} +(-0.470363 + 0.830516i) q^{55} +(0.108326 + 0.120308i) q^{56} +(1.47892 - 1.70333i) q^{57} +(-1.58694 + 0.337315i) q^{58} +(-5.94695 - 2.64775i) q^{59} +(3.48285 - 6.41694i) q^{60} +(9.05256 - 4.03046i) q^{61} +(1.83510 - 1.33328i) q^{62} +(0.357816 - 0.0896624i) q^{63} +(4.34781 + 3.15887i) q^{64} +(-8.35529 + 1.84848i) q^{65} +(0.227007 - 0.106018i) q^{66} +(-7.58023 + 1.61123i) q^{67} +(-4.07984 - 7.06649i) q^{68} +(6.69688 - 12.0983i) q^{69} +(0.0472544 + 0.0803024i) q^{70} +(1.29478 + 3.98492i) q^{71} +(-3.54804 + 1.73568i) q^{72} +(-8.67115 - 6.29996i) q^{73} +(1.12129 - 1.94214i) q^{74} +(5.56860 - 6.63255i) q^{75} +(1.22759 + 2.12625i) q^{76} +(0.00548619 - 0.0521976i) q^{77} +(2.06822 + 0.876467i) q^{78} +(6.30512 + 1.34020i) q^{79} +(5.01927 + 5.48239i) q^{80} +(-0.292856 + 8.99523i) q^{81} +2.15982 q^{82} +(-1.73857 - 1.93088i) q^{83} +(-0.0347558 + 0.399980i) q^{84} +(-3.06703 - 9.17973i) q^{85} +(-0.123539 + 1.17539i) q^{86} +(-6.79537 - 4.75220i) q^{87} +(0.0587443 + 0.558914i) q^{88} +(4.89782 + 3.55847i) q^{89} +(-2.20046 + 0.570821i) q^{90} +(0.380691 - 0.276588i) q^{91} +(10.0708 + 11.1847i) q^{92} +(11.3818 + 2.20542i) q^{93} +(-1.79215 + 0.380933i) q^{94} +(0.922843 + 2.76211i) q^{95} +(-0.797430 - 6.46301i) q^{96} +(-13.6699 - 2.90563i) q^{97} +(1.91498 + 1.39132i) q^{98} +(1.18787 + 0.478299i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9}+O(q^{10}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20} + 15 q^{21} - 11 q^{22} + q^{23} - 30 q^{24} - 16 q^{25} - 136 q^{26} + 7 q^{27} + 4 q^{28} - 15 q^{29} - 24 q^{30} + 3 q^{31} + 12 q^{32} - 5 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} - 24 q^{37} + 55 q^{38} + 20 q^{39} + q^{40} - 19 q^{41} - 38 q^{42} - 8 q^{43} + 4 q^{44} - 38 q^{45} - 20 q^{46} - 10 q^{47} - 25 q^{48} - 72 q^{49} - 3 q^{50} - 26 q^{51} - 25 q^{52} - 12 q^{53} + 53 q^{54} - 20 q^{55} - 60 q^{56} + 38 q^{57} - 23 q^{58} - 30 q^{59} - 33 q^{60} - 3 q^{61} - 44 q^{62} + 46 q^{63} - 44 q^{64} + 51 q^{65} - 134 q^{66} - 12 q^{67} - 156 q^{68} + 4 q^{69} - 16 q^{70} + 42 q^{71} + 74 q^{72} - 12 q^{73} + 90 q^{74} + 67 q^{75} - 8 q^{76} + 31 q^{77} - 92 q^{78} - 15 q^{79} + 298 q^{80} - 104 q^{81} + 8 q^{82} + 59 q^{83} + 115 q^{84} - 11 q^{85} + 9 q^{86} - 59 q^{87} - 23 q^{88} + 106 q^{89} + 107 q^{90} + 30 q^{91} + 11 q^{92} + 32 q^{93} + 25 q^{94} + 7 q^{95} + 35 q^{96} - 21 q^{97} + 146 q^{98} - 20 q^{99}+O(q^{100}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9 - 20 * q^10 - 11 * q^11 - 4 * q^12 - 3 * q^13 + q^14 - 48 * q^15 + 23 * q^16 - 24 * q^17 - 12 * q^19 + q^20 + 15 * q^21 - 11 * q^22 + q^23 - 30 * q^24 - 16 * q^25 - 136 * q^26 + 7 * q^27 + 4 * q^28 - 15 * q^29 - 24 * q^30 + 3 * q^31 + 12 * q^32 - 5 * q^33 + q^34 + 14 * q^35 + 38 * q^36 - 24 * q^37 + 55 * q^38 + 20 * q^39 + q^40 - 19 * q^41 - 38 * q^42 - 8 * q^43 + 4 * q^44 - 38 * q^45 - 20 * q^46 - 10 * q^47 - 25 * q^48 - 72 * q^49 - 3 * q^50 - 26 * q^51 - 25 * q^52 - 12 * q^53 + 53 * q^54 - 20 * q^55 - 60 * q^56 + 38 * q^57 - 23 * q^58 - 30 * q^59 - 33 * q^60 - 3 * q^61 - 44 * q^62 + 46 * q^63 - 44 * q^64 + 51 * q^65 - 134 * q^66 - 12 * q^67 - 156 * q^68 + 4 * q^69 - 16 * q^70 + 42 * q^71 + 74 * q^72 - 12 * q^73 + 90 * q^74 + 67 * q^75 - 8 * q^76 + 31 * q^77 - 92 * q^78 - 15 * q^79 + 298 * q^80 - 104 * q^81 + 8 * q^82 + 59 * q^83 + 115 * q^84 - 11 * q^85 + 9 * q^86 - 59 * q^87 - 23 * q^88 + 106 * q^89 + 107 * q^90 + 30 * q^91 + 11 * q^92 + 32 * q^93 + 25 * q^94 + 7 * q^95 + 35 * q^96 - 21 * q^97 + 146 * q^98 - 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more